Статті в журналах: "NCF (Noise Correlation Function)"

1

Peng, Hanshu, Zhongliang Wu, and Changsheng Jiang. "Pre-seismic changes of noise correlation function (NCF) before the Wenchuan earthquake?" Concurrency and Computation: Practice and Experience 22, no. 12 (September 25, 2009): 1774–83. http://dx.doi.org/10.1002/cpe.1517.

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Kuponiyi, Ayodeji Paul, and Honn Kao. "Temporal Variation in Cultural Seismic Noise and Noise Correlation Functions during COVID-19 Lockdown in Canada." Seismological Research Letters 92, no. 5 (April 28, 2021): 3024–34. http://dx.doi.org/10.1785/0220200330.

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Abstract The COVID-19 pandemic of 2020 led to a widespread lockdown that restricted human activities, particularly land, air, and maritime traffic. The “quietness” on land and ocean that followed presents an opportunity to measure an unprecedented reduction in human-related seismic activities and study its effect on the short-period range of ambient noise cross-correlation functions (NCFs). We document the variations in seismic power levels and signal quality of short-period NCFs measured by four seismographs located near Canadian cities across the pandemic-defined timeline. Significant drops in seismic power levels are observed at all the locations around mid-March. These drops coincide with lockdown announcements by the various Canadian provinces where the stations are located. Mean seismic power reductions of ∼24% and ∼17% are observed near Montreal and Ottawa, respectively, in eastern Canada. Similar reductions of ∼27% and 17% are recorded in western Canada near Victoria and Sidney, respectively. None of the locations show full recovery in seismic power back to the pre-lockdown levels by the end of June, when the provinces moved into gradual reopening. The overall levels of seismic noise during lockdown are a factor of 5–10 lower at our study locations in western Canada, relative to the east. Signal quality of NCF measured in the secondary microseism frequency band for the station pair in western Canada is maximum before lockdown (late February–early March), minimum during lockdown (mid–late March), and increased to intermediate levels in the reopening phase (late May). A similar pattern is observed for the signal quality of the eastern Canada station pair, except for a jump in levels at similar periods during the lockdown phase. The signal quality of NCF within the secondary microseism band is further shown to be the lowest for the western Canada station pair during the 2020 lockdown phase, when compared with similar time windows in 2018 and 2019.

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Hawkins, Rhys, and Malcolm Sambridge. "An Adjoint Technique for Estimation of Interstation Phase and Group Dispersion from Ambient Noise Cross Correlations." Bulletin of the Seismological Society of America 109, no. 5 (July 16, 2019): 1716–28. http://dx.doi.org/10.1785/0120190060.

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Abstract A method of extracting group and phase velocity dispersions jointly for Love‐ and Rayleigh‐wave observations is presented. This method uses a spectral element representation of a path average Earth model parameterized with density, shear‐wave velocity, radial anisotropy, and VP/VS ratio. An initial dispersion curve is automatically estimated using a heuristic approach to prevent misidentification of the phase. A second step then more accurately fits the observed noise correlation function (NCF) between interstation pairs in the frequency domain. For good quality cross correlations with reasonable signal‐to‐noise ratio, we are able to very accurately fit the spectrum of NCFs and hence obtain reliable estimates of both phase and group velocity jointly for Love and Rayleigh surface waves. In addition, we also show how uncertainties can be estimated with linearized approximations from the Jacobians and subsequently used in tomographic inversions.

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Jiang, Changsheng, and Zhongliang Wu. "Temporal variation of noise correlation function (NCF) in Beijing and surroundings: Its relation with climate events and implications." Earthquake Science 22, no. 1 (February 2009): 75–81. http://dx.doi.org/10.1007/s11589-009-0075-5.

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5

Ragland, John, and Shima Abadi. "Exploring surface source distributions for ocean ambient noise interferometry with airgun shots." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A190. http://dx.doi.org/10.1121/10.0011063.

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Ambient noise interferometry utilizes the cross-correlations of ambient sound to estimate the time domain Green’s function (TDGF). We have previously shown that ambient noise interferometry can resolve multi-path arrivals between two bottom-mounted hydrophones separated by 3.2 km, at a depth of 1500 m, and located 470 km off the Oregon coast. In 2019, a seismic reflection survey was conducted directly over the two hydrophones for 28 days covering a 763 km2 area. The airgun shots occurred every 37.5 m while the ship moved at a speed of ∼4.5 knots, equivalent to a shooting interval of 16 s. The hydrophone recordings during this survey provide the unique opportunity to understand the effects of the surface source distribution on the noise cross correlation function (NCCF). In this talk, we show the sensitivity of the NCCF to the surface source locations using simulated and experimental data. Then, we use the image source method to analytically define the location of the sound sources that contribute to different delay times in the NCCF. [Work supported by ONR.]

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Steinmann, René, Céline Hadziioannou, and Eric Larose. "Effect of centimetric freezing of the near subsurface on Rayleigh and Love wave velocity in ambient seismic noise correlations." Geophysical Journal International 224, no. 1 (August 28, 2020): 626–36. http://dx.doi.org/10.1093/gji/ggaa406.

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SUMMARY About a decade ago, noise-based monitoring became a key tool in seismology. One of the tools is passive image interferometry (PII), which uses noise correlation functions (NCF) to retrieve seismic velocity variations. Most studies apply PII to vertical components recording oceanic low-frequent ambient noise ( < 1 Hz). In this work, PII is applied to high-frequent urban ambient noise ( > 1 Hz) on three three-component sensors. With environmental sensors inside the subsurface and in the air, we are able to connect observed velocity variations with environmental parameters. Temperatures below 0 °C correlate well with strong shear wave velocity increases. The temperature sensors inside the ground suggest that a frozen layer of less than 5 cm thickness causes apparent velocity increases above 2 % , depending on the channel pair. The observations indicate that the different velocity variation retrieved from the different channel pairs are due to different surface wave responses inherent in the channel pairs. With dispersion curve modelling in a 1-D medium we can verify that surfaces waves of several tens of metres wavelength experience a velocity increase of several percent due to a centimetres thick frozen layer. Moreover, the model verifies that Love waves show larger velocity increases than Rayleigh waves. The findings of this study provide new insights for monitoring with PII. A few days with temperature below 0 °C can already mask other potential targets (e.g. faults or storage sites). Here, we suggest to use vertical components, which is less sensitive to the frozen layer at the surface. If the target is the seasonal freezing, like in permafrost studies, we suggest to use three-component sensors in order to retrieve the Love wave response. This opens the possibility to study other small-scale processes at the shallow subsurface with surface wave responses.

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Tian, Jinyu, Jian Lin, Fan Zhang, Min Xu, Yayun Zhang, Laiyin Guo, and Xin Zeng. "Time Correction of Ocean-Bottom Seismometers Using Improved Ambient Noise Cross Correlation of Multicomponents and Dual-Frequency Bands." Seismological Research Letters 92, no. 3 (January 13, 2021): 2004–14. http://dx.doi.org/10.1785/0220200358.

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Abstract An effective approach was developed for identifying and correcting ocean-bottom seismometer (OBS) time errors through improving ambient noise cross-correlation function (NCCF) analysis and combination with other methods. Significant improvements were illustrated through analyzing data from a passive-source seismic experiment in the southwestern sub-basin of the South China Sea. A novel method was first developed that can effectively identify errors in the sampling frequency of the OBS instruments. The traditional NCCF method was then expanded by increasing the analyzed data spectrum from a single-frequency band to dual-frequency band pairs, thus doubling the number of available data points and substantially improving the time correction quality. For data with relatively low signal-to-noise ratios, the average time errors were reduced from the original average values of 60–80 ms by the conventional methods to <40 ms using the improved approaches. The new multistep procedure developed in this study has general applicability to analysis of other OBS experiments. The demonstrated significant improvements in the data quality are critical for advancing seismic tomography and other modern marine geophysical studies that require high accuracy in the OBS data.

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Cheng, Wei, Lintao Liu, and Guocheng Wang. "A new method for estimating the correlation of seismic waveforms based on the NTFT." Geophysical Journal International 226, no. 1 (April 1, 2021): 368–76. http://dx.doi.org/10.1093/gji/ggab047.

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SUMMARY We propose a new correlation function called the similarity coefficient (SC) based on the normal time–frequency transform (NTFT) to evaluate the similarity between two non-stationary seismic signals as a function of the delay time. The SC is defined in the time–frequency spectrum of the NTFT, and the instantaneous phase and amplitude of each frequency component in a signal are used to calculate the SC. Our simulation experiments demonstrate that the SC method can effectively recognize similar signals compared to the conventional normalized cross-correlation coefficient (NCC) under high background noise conditions. The SC presents good robustness in identifying similar signals and performs well in the case of an extremely low signal-to-noise ratio (SNR), which makes it suitable for detecting weak seismic signals concealed by noise. As a real application case, we use the SC method to detect quasi-Love (QL) surface waves. QL waves are scattered Love waves and are important indicators for lateral anisotropic gradients in the upper mantle. We detect the QL waves at 21 stations deployed across Japan after the 23 December 2004 Mw 8.1 Macquarie earthquake by using the SC method. Obvious QL waves are observed at 19 stations, and we locate the Love-to-Rayleigh scatterers by applying the delay times between the QL and main Love waves. Our results show that the QL wave scatterers were mostly generated in two areas: Mariana subduction and Papua New Guinea. The observations of QL waves suggest the presence of lateral gradients in anisotropy beneath those two areas. The spatial distribution of the 13 scatterers in the Mariana subduction zone agrees well with the Mariana Island Arc, and we infer that the Mariana slab may have melted and coupled with the surrounding mantle at depth.

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Wang, Jian, Xiaolei Lv, Zenghui Huang, and Xikai Fu. "An Epipolar HS-NCC Flow Algorithm for DSM Generation Using GaoFen-3 Stereo SAR Images." Remote Sensing 15, no. 1 (December 26, 2022): 129. http://dx.doi.org/10.3390/rs15010129.

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Radargrammetry is a widely used methodology to generate the large-scale Digital Surface Model (DSM). Stereo matching is the most challenging step in radargrammetry due to the significant geometric differences and the inherent speckle noise. The speckle noise results in significant grayscale differences of the same feature points, which makes the traditional Horn–Schunck (HS) flow or multi-window zero-mean normalized cross-correlation (ZNCC) methods degrade. Therefore, this paper proposes an algorithm named Epipolar HS-NCC Flow (EHNF) for dense stereo matching, which is an improved HS flow method with normalized cross-correction constraint based on epipolar stereo images. First, the epipolar geometry is applied to resample the image to realize the coarse stereo matching. Subsequently, the EHNF method forms a global energy function to achieve fine stereo matching. The EHNF method constructs a local normalized cross-correlation constraint term to compensate for the grayscale invariance constraint, especially for the SAR stereo images. Additionally, two assessment methods are proposed to calculate the optimal cross-correlation parameter and smoothness parameter according to the refined matched point pairs. Two GaoFen-3 (GF-3) image pairs from ascending and descending orbits and the open Light Detection and Ranging (LiDAR) data are utilized to fully evaluate the proposed method. The results demonstrate that the EHNF algorithm improves the DSM elevation accuracy by 9.6% and 27.0% compared with the HS flow and multi-window ZNCC methods, respectively.

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Perez-Cham, Oscar E., Cesar Puente, Carlos Soubervielle-Montalvo, Gustavo Olague, Carlos A. Aguirre-Salado, and Alberto S. Nuñez-Varela. "Parallelization of the Honeybee Search Algorithm for Object Tracking." Applied Sciences 10, no. 6 (March 20, 2020): 2122. http://dx.doi.org/10.3390/app10062122.

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Object tracking refers to the relocation of specific objects in consecutive frames of a video sequence. Presently, this visual task is still considered an open research issue, and the computer science community attempted solutions from the standpoint of methodologies, algorithms, criteria, benchmarks, and so on. This article introduces a GPU-parallelized swarm algorithm, called the Honeybee Search Algorithm (HSA), which is a hybrid algorithm combining swarm intelligence and evolutionary algorithm principles, and was previously designed for three-dimensional reconstruction. This heuristic inspired by the search for food of honeybees, and here adapted to the problem of object tracking using GPU parallel computing, is extended from the original proposal of HSA towards video processing. In this work, the normalized cross-correlation (NCC) criteria is used as the fitness function. Experiments using 314 video sequences of the ALOV benchmark provides evidence about the quality regarding tracking accuracy and processing time. Also, according to these experiments, the proposed methodology is robust to high levels of Gaussian noise added to the image frames, and this confirms that the accuracy of the original NCC is preserved with the advantage of acceleration, offering the possibility of accelerating latest trackers using this methodology.

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Dr. R. Balasubrimanian, V. Belmer Gladson,. "A Novel Fuzzy Inference System Based Robust Reversible Watermarking Technique provided with Six Layer Security." INFORMATION TECHNOLOGY IN INDUSTRY 9, no. 2 (March 30, 2021): 661–78. http://dx.doi.org/10.17762/itii.v9i2.398.

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Digital Watermarking has evolved as one of the latest technologies for digital media copyright protection. Watermarking of images can be done in many ways and one of the proposed algorithms for image watermarking is by utilizing Fuzzy Logic. It is similar to the concept of a Fuzzy set, each element can be defined by an ordered pair, in which one is the value and other is the membership function value. Fuzzy logic systems can explain inaccurate information and explain their decisions. Fuzzy inference system is the simplest way of performing Fuzzy Logic. In the proposed method, three Fuzzy inference models are used to generate the weighing factor for embedding the watermark and input to the Fuzzy Inference System is taken from the Human Visual System model. The Performance measures used in the Process are Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM), Normalized Cross Correlation (NCC) and Bit Error Ratio (BER). The Proposed algorithm is immune to various Image Processing attacks.

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Agrawal, Sushama, and Anjali Bhalchandra. "Firefly optimized robust, imperceptible, secure watermarking scheme." Indonesian Journal of Electrical Engineering and Computer Science 28, no. 2 (November 1, 2022): 1155. http://dx.doi.org/10.11591/ijeecs.v28.i2.pp1155-1163.

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A multi-objective optimized hybrid image watermarking technique is being proposed considering robustness, imperceptibility and security aspects using two different scaling factors. In this technique, original image is subjected to third level lifting wavelet transform (LWT) followed by singular value decomposition (SVD). Watermark is split into two parts to embed each of them into a different subband. In the suggested scheme, firefly algorithm is employed to get optimum solutions for two scaling factors to balance trade-off amid invisibility and robustness. Security in digitized data is an important aspect of image processing. It is improved with a key, an input to Arnold transform for scrambling watermark, to watermark embedding and extraction procedures. All the performance parameters like peak signal to noise ratio (PSNR), structural similarity index measure (SSIM), normalized correlation coefficient (NCC) and bit error rate (BER) are used in formulating maximization objective function. Evaluation of the proposed algorithm indicates that it is characterized by fairly good robustness, invisibility and security.

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Li, J., S. M. Bentzen, M. Renschler, and M. P. Mehta. "Improvement in neurocognitive function (NCF) correlates with tumor regression after whole brain radiation therapy (WBRT) for brain metastases (BM)." Journal of Clinical Oncology 24, no. 18_suppl (June 20, 2006): 1504. http://dx.doi.org/10.1200/jco.2006.24.18_suppl.1504.

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1504 Background: Few prospective trials have explored the neurocognitive impact of WBRT in BM patients (pts), complicated by competing effects between benefit from WBRT and deterioration due to disease progression. Methods: 208 pts from the WBRT alone arm (30 Gy) of a phase III trial (PCYC-9801) evaluating motexafin gadolinium in BM were analyzed. NCF was assessed by 8 tests of memory, executive function and fine motor coordination, and correlated to BM volume change by MRI, using Spearman’s rank correlation. Pts with tumor shrinkage below and above the median (45%) were compared for survival and NCF deterioration using Kaplan-Meier analysis. Results: 135 pts (65%) were evaluable for BM volume at baseline and 2 months (mo). Pts were divided into “good” and “poor” responders based on % volume reduction at 2 mo above or below the population median of 45%. The uni-directional hypothesis of improved survival in good responders was significant (P = 0.03, median survival (MS) 300±26 days (d) vs 240±19 d). For all 8 tests, the median time to NCF deterioration was longer in good responders than in poor responders. Largest gains were for an executive function test Trailmaking B (131 d gain, P=0.02), fine motor tests Pegboard non-dominant hand (110 d gain, P=0.05) and Pegboard dominant hand (93 d gain, P=0.02). In 15 mo survivors, statistically significant correlation between tumor shrinkage and NCF preservation was seen for 4/8 NCF tests (r = 0.68–0.88), especially for executive function and fine motor coordination. At early follow-up, the population mean NCF scores were dominated by pts with progressive disease, as reflected by a sharp drop in the mean NCF scores at 4 mo. 15-mo survivors had stable or improving scores, associated with greater reduction in BM volume in the 15 versus 4 mo survivors. Conclusions: WBRT-induced tumor shrinkage correlates with better survival and NCF preservation. NCF is stable or improved in long-term BM survivors. The adverse impact of tumor growth on neurocognitive function appears greater than that of WBRT. [Table: see text]

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Zarrella, Giuliana, Michael Parsons, Janet Sherman, Jorg Dietrich, and Helen Shih. "NCOG-20. LONGITUDINAL ASSESSMENT OF SUBJECTIVE COGNITIVE FUNCTION IN ADULTS WITH LOW GRADE GLIOMA TREATED WITH PROTON RADIATION THERAPY." Neuro-Oncology 23, Supplement_6 (November 2, 2021): vi156. http://dx.doi.org/10.1093/neuonc/noab196.611.

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Abstract INTRODUCTION Our group previously demonstrated stability in neurocognitive function (NCF) over a 5-year period after proton radiation therapy (PRT) in low grade glioma (LGG) patients. Subjective cognitive function (SCF) had not been previously explored, nor had individual analyses of cognition, which can detect variability in trajectory. We used the newly derived Functional Assessment of Cancer Therapy-Brain Cognitive-Index (FACT-Br-CI) to examine SCF in LGG patients after PRT and compare longitudinal changes in SCF and NCF. METHODS 20 LGG patients (M age =37.5) treated with PRT completed NCF tests and self-report measures annually for 5 years or until tumor progression. Group change in SCF was examined with paired t-test (baseline vs final FACT-Br-CI). Individual change scores were calculated for FACT-Br-CI and NCF tests (clinical trials battery composite; CTBC). Individual deterioration in NCF was defined by reliable change index (RCI) on CTBC, and in SCF was defined as decline of >/=1 SD in FACT-Br-CI. Relationships between change in SCF and NCF were explored with correlations. RESULTS At the group level, no change was observed in FACT-Br-CI between baseline and last follow-up (t(19)=-.91;p=ns). Individual SCF analyses at last follow-up found the number of patients reporting decline=3 (15%), improvement=5 (25%), and no change=12 (60%). Individual changes were observed in SCF in 20% of patients at 3 months, 5.9% at 6 months, 12.5% at 12 months, 13.3% at 24 months, and 11.1% at 36 months. Median time to any deterioration in SCF was 36 months and for NCF was not reached. Correlation between CTBC and FACT-Br-CI change scores did not reach statistical significance (r=.41;p=ns). CONCLUSION Consistent with previous research, group analyses of LGG patients did not show cognitive decline after PRT. However individual analyses of SCF showed variability within the group: some patients experienced cognitive decline during follow up. Consideration of individual differences may yield additional information.

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Makarewicz, Aleksandra, Małgorzata Jamka, Maria Wasiewicz-Gajdzis, Joanna Bajerska, Anna Miśkiewicz-Chotnicka, Jarosław Kwiecień, Aleksandra Lisowska, et al. "Comparison of Subjective and Objective Methods to Measure the Physical Activity of Non-Depressed Middle-Aged Healthy Subjects with Normal Cognitive Function and Mild Cognitive Impairment—A Cross-Sectional Study." International Journal of Environmental Research and Public Health 18, no. 15 (July 29, 2021): 8042. http://dx.doi.org/10.3390/ijerph18158042.

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This study compared subjective and objective methods of measuring different categories of physical activity in non-depressed middle-aged subjects with normal cognitive function (NCF) and mild cognitive impairment (MCI). In total, 75 participants (NCF: n = 48, MCI: n = 27) were recruited and physical activity was assessed for seven days using the ActiGraph and the International Physical Activity Questionnaire (IPAQ). Anthropometric parameters, body compositions, resting metabolic rate, and energy expenditure were also assessed. ActiGraph data indicated that subjects with NCF were more active than MCI subjects. A comparison of the IPAQ and the ActiGraph data revealed a significant correlation between these methods for total (r = 0.3315, p < 0.01) and moderate (r = 0.3896, p < 0.01) physical activity in the total population and moderate activity (r = 0.2893, p < 0.05) within the NCF group. No associations between these methods were found within the MCI group. Independent predictors of subjectively evaluated total physical activity were alcohol consumption (p = 0.0358) and socio-professional status (p = 0.0288), while weight (p = 0.0285) and the Montreal Cognitive Assessment results (p = 0.0309) were independent predictors of objectively measured physical activity. In conclusion, the long version of IPAQ is a more reliable tool to assess PA in subjects with NCF than those with MCI. More studies are needed to confirm this finding.

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Gardner, Melissa, Giuliana Zarrella, Jorg Dietrich, and Michael Parsons. "NCOG-48. LONGITUDINAL ASSESSMENT OF SUBJECTIVE COGNITIVE FUNCTION IN A BRAIN TUMOR SAMPLE: IMPROVED CORRESPONDENCE WITH NEUROPSYCHOLOGICAL PERFORMANCE OVER TIME." Neuro-Oncology 23, Supplement_6 (November 2, 2021): vi162. http://dx.doi.org/10.1093/neuonc/noab196.637.

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Abstract INTRODUCTION Estimates of subjective cognitive function (SCF) generally show minimal correlation with objective measures of neurocognitive function (NCF). Our group recently validated a new metric of SCF in neuro-oncology patients, creating the Cognitive Index of the Functional Assessment of Cancer Therapy-Brain (FACT-Br-CI). This study examines whether brain tumor (BT) patients evaluated on more than one occasion show improved relationship between SCF and NCF. We hypothesized that change scores in SCF and NCF across evaluation would be more highly correlated than SCF and NCF at either timepoint. METHODS A retrospective study of BT patients who completed two neuropsychological evaluations (baseline, follow-up) was conducted. NCF was measured by the clinical trial battery composite (CTBC), a mean of 6 commonly used neuropsychological test scores. SCF was measured by the FACT-Br-CI. Mood/Anxiety were measured by the Beck scales (BAI/BDI-II). Change over time on each metric was evaluated with paired t-test. Correlational analyses evaluated relationships between NCF, SCF, and mood within and between time points. RESULTS Twenty-nine patients (16 female; mean age=54.6y; mean education=15.5y) completed all CTBC measures and FACT-Br-CI, 28 of whom completed and BDI and/or BAI. On group analyses, there were no significant differences between baseline and follow-up on CTBC (t=-.53;p=ns) or FACT-Br-CI (t=-.98;p=ns). Correlations between CTBC and FACT-Br-CI were nonsignificant at baseline (r=.24;p=ns), but significant at follow-up (r=.56;p=0.002). Change scores over time were unrelated (r=-.104;p=ns). Similar to previous studies, the FACT-BR-CI correlated with the BDI-II at baseline (r=-.38;p=0.04) and follow-up (r=-.59;p< 0.001) and with the BAI at follow-up (r=-.44;p=0.02). CONCLUSION In this small group of brain tumor patients seen for repeated neuropsychological evaluations, we found that agreement between SCF and NCF was much higher on their second than initial evaluation. These findings suggest that patients may develop enhanced awareness of their cognitive function from an initial evaluation that persists over time.

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Hooge, F. N., and P. A. Bobbert. "On the correlation function of 1/f noise." Physica B: Condensed Matter 239, no. 3-4 (August 1997): 223–30. http://dx.doi.org/10.1016/s0921-4526(97)00332-3.

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Yanovskaya, T. B., and T. Yu Koroleva. "Effect of earthquakes on ambient noise cross-correlation function." Izvestiya, Physics of the Solid Earth 47, no. 9 (August 23, 2011): 747–56. http://dx.doi.org/10.1134/s1069351311090059.

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Skarsoulis, Emmanuel, and Bruce Cornuelle. "Green’s function emergence through cross-correlation of shipping noise." Journal of the Acoustical Society of America 144, no. 3 (September 2018): 1731. http://dx.doi.org/10.1121/1.5067677.

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Aliev, T. A., N. F. Musaeva, Q. A. Quluyev, and N. E. Rzayeva. "Technologies for Analyzing and Calculating the Relationship between the Useful Component and the Noise of Noisy Signal in Monitoring Systems." Mekhatronika, Avtomatizatsiya, Upravlenie 23, no. 12 (December 7, 2022): 628–36. http://dx.doi.org/10.17587/mau.23.629-636.

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The article is devoted to the development of algorithms for calculating the cross-correlation function and the correlation coefficient between the useful signal and the noise of a noisy signal. The authors analyze the factors influencing the adequacy of the results of solving the problems of monitoring, control, management, etc. It is noted that when processing noisy signals, algorithms and technologies for separate processing of the useful component and the noise should be used. It is shown that in the event of malfunctions, such an important condition as the absence of correlation between the useful signal and the noise is violated in monitoring and control systems. Therefore, the problem arises of calculating the crosscorrelation function and the correlation coefficient between the useful signal and the total noise as well. Algorithms are proposed for calculating the estimates of the correlation coefficient and the correlation function between the useful signal and the noise of noisy signals. It is pointed out that the moment of occurrence of the correlation between the useful signal and the noise can be monitored in real time in information systems. It is shown that the estimate of the variance of the total noise before the appearance of the correlation is a stable value. When a correlation appears, the value of the variance of the total noise changes. The difference in the variance estimates is taken as an analogue of the estimate of the cross-correlation function between the useful signal and the noise at zero time shift.A technology for conducting computational experiments is proposed. Discrete values of the useful signal, noise and noisy signal are generated. The correlation coefficient and the cross-correlation function between the useful signal and the noise are calculated by the developed and traditional algorithms. A comparative analysis is carried out. It is shown that the proposed technologies for calculating the estimates of the cross-correlation function and the correlation coefficient between the useful signal and the noise, as well as the variance of the total noise, make it possible to extract additional important information from noisy signals. This opens up the opportunity to increase the efficiency of the analysis of noisy signals.

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Wang, Zhong-long, Li Cao, and Jun-lin Qiu. "Correlation Function and Time-Dependent Moments of the Intensity for Gain-Noise Model of a Single-Mode Laser with Exponential Function Correlation Noise." Chinese Physics Letters 15, no. 7 (July 1, 1998): 498–500. http://dx.doi.org/10.1088/0256-307x/15/7/011.

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WANG, CAN-JUN, and DONG-CHENG MEI. "THE RELAXATION TIME AND THE CORRELATION FUNCTION FOR A LOGISTIC GROWTH SYSTEM DRIVEN BY COLORED CROSS-CORRELATION NOISES." Fluctuation and Noise Letters 08, no. 02 (June 2008): L213—L228. http://dx.doi.org/10.1142/s0219477508004398.

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The associated relaxation time Tc and the normalized correlation function C(s) are investigated in the logistic growth system, which is used to describe a tumor cell growth process, driven by two Gaussian white noise sources and the correlation between the additive and multiplicative noise. The expression of Tc and C(s), which is the function of noise parameters (additive noise intensity α, multiplicative noise intensity D, correlation intensity λ and correlation time τ), is obtained by using the projection operator method. After introducing noise intensity ratio, a dimensionless parameter R = α/D, and performing the numerical computations, the two case are analyzed: (1) In the growth case, λ and τ play opposite roles on the Tc and the C(s). It must emphasize that there is a minimal evolution velocity to appear and the tumor cell numbers is hard to evolve from an arbitrary initial condition to the maximum. (2) In the decay case, λ and τ play same roles on the Tc and the C(s). There is a maximal evolution velocity to appear. The noises induce different responses of tumor cells between the growth and decay case.

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23

Ohtsubo, J., and M. Kourogi. "Frequency correlation function of modal noise in multimode optical fibers." Journal of Lightwave Technology 7, no. 9 (1989): 1300–1307. http://dx.doi.org/10.1109/50.50708.

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24

Cheng, Qing-Hua, Li Cao, Da-Hai Xu, and Da-Jin Wu. "Influence of Noise on Time Evolution of Intensity Correlation Function." Communications in Theoretical Physics 44, no. 5 (November 2005): 867–72. http://dx.doi.org/10.1088/6102/44/5/867.

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25

Muhammad, Ghulam. "Noise-Robust Pitch Detection using Auto-correlation Function with Enhancements." Journal of King Saud University - Computer and Information Sciences 22 (2010): 13–28. http://dx.doi.org/10.1016/s1319-1578(10)80002-3.

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26

Dumusque, Xavier, Cristophe Lovis, Stephane Udry, and Nuno C. Santos. "Stellar noise and planet detection. II. Radial-velocity noise induced by magnetic cycles." Proceedings of the International Astronomical Union 6, S276 (October 2010): 530–32. http://dx.doi.org/10.1017/s1743921311021090.

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AbstractFor the 451 stars of the HARPS high precision program, we study correlations between the radial-velocity (RV) variation and other parameters of the Cross Correlated Function (CCF). After a careful target selection, we found a very good correlation between the slope of the RV-activity index (log(R'HK)) correlation and the Teff for dwarf stars. This correlation allow us to correct RV from magnetic cycles given the activity index and the Teff.

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27

Mahmoudzadeh, Amir Pasha, and Nasser H. Kashou. "Evaluation of Interpolation Effects on Upsampling and Accuracy of Cost Functions-Based Optimized Automatic Image Registration." International Journal of Biomedical Imaging 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/395915.

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Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.

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28

Aliev, Telman, and Nailya Musaeva. "TECHNOLOGIES FOR CALCULATING THE CORRELATION COEFFICIENT BETWEEN THE USEFUL SIGNAL AND THE NOISE USING THE ESTIMATE OF THEIR RELAY CROSS-CORRELATION FUNCTION." Journal of Automation and Information sciences 5 (September 1, 2021): 93–103. http://dx.doi.org/10.34229/1028-0979-2021-5-8.

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It is shown that when noisy signals are formed, the condition for the absence of correlation between the useful signal and the noise is often violated. This causes certain errors of correlation analysis of these signals, resulting in the inadequacy of the results obtained. In addition, the existing correlation analysis technologies do not allow using the noise as a carrier of valuable information. Therefore, the full use of the colossal information potential of noisy signals requires new technologies that would exclude the loss of valuable information, both when the known classical conditions are met and when they are not. Algorithms are developed for determining the estimate of the correlation coefficient between the useful signal and the noise, which cannot be measured directly or isolated from a noisy signal. For this purpose, the normalized cross-correlation function between the useful signal and the noise is used. An algorithm for calculating the estimates of the normalized cross-correlation function between the useful signal and the noise is developed using the estimates of the relay correlation function of the noisy signal. It is shown that the value of this estimate, calculated at a zero time shift, is an estimate of the correlation coefficient between the useful signal and the noise. A technology for conducting computational experiments is proposed, a comparative analysis is carried out, and the reliability of the proposed algorithms and technologies is confirmed. It is shown that under the normal technical condition of the object, the estimates of the relay cross-correlation function and the correlation coefficient between the useful signal and the noise will be close to zero. With the emergence of various defects preceding malfunctions at the object, these estimates will change depending on the degree of damage. Therefore, it is the estimates of the cross-correlation function and the correlation coefficient between the useful signal and the noise that should be used in monitoring and control systems as informative attributes for signaling and monitoring the beginning of changes in the technical condition of objects and the dynamics of their malfunctions. The use of these new effective informative attributes makes it possible to increase the degree of accuracy and reliability of operation of modern information systems.

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29

Ng, Kin-Wang. "Correlation Functions of CMB Anisotropy and Polarization." Symposium - International Astronomical Union 183 (1999): 104. http://dx.doi.org/10.1017/s0074180900132231.

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While the temperature anisotropy of the cosmic microwave background is proved to be a promising tool for probing the early Universe, the CMB polarization is another important clue for extracting more cosmic information. We give a full analysis of the auto- and cross-correlations between the CMB Stokes parameters. In particular, we derive the windowing function for an antenna with Gaussian response in polarization experiment, and construct correlation function estimators corrected for instrumental noise. They are applied to calculate the signal to noise ratios for future MAP and Planck anisotropy and polarization measurements.

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30

Cornuelle, Bruce D., and Emmanuel K. Skarsoulis. "Peak-time sensitivity kernels for noise cross-correlation envelopes." Journal of the Acoustical Society of America 151, no. 4 (April 2022): 2353–66. http://dx.doi.org/10.1121/10.0010044.

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The envelope of the time-lagged cross-correlation of an underwater noise field between two hydrophones can under certain conditions be used as a proxy for active acoustic receptions between the two locations enabling the study of ocean variability. Previous work looked at the sensitivity of cross-correlation peak amplitudes with respect to the distribution of the noise sources. The present study examines the sensitivity of the cross-correlation envelope peak times with respect to changes in the sound-speed distribution. A wave-theoretic scheme allowing for finite-frequency calculations in two and three dimensions, combined with the Born approximation for perturbations of the Green's function and the peak arrival approach, is used to obtain sensitivity kernels with respect to environmental (sound-speed) changes. These kernels provide a way to infer ocean structure from the cross-correlation peaks, considered as observables on their own and valid even in cases where the cross-correlation function does not approximate the time-domain Green's function between the two receivers. The sensitivity behavior is studied for different propagation conditions and noise-source distributions, ranging from spatially distributed uncorrelated noise sources to point sources, such as individual ships. Deviations from linearity are addressed and discussed.

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31

Song, Seong Jun, Hyun Joon Shim, Chul Ho Park, Seong Hee Lee, and Sang Won Yoon. "Analysis of Correlation between Cognitive Function and Speech Recognition in Noise." Korean Journal of Otorhinolaryngology-Head and Neck Surgery 53, no. 4 (2010): 215. http://dx.doi.org/10.3342/kjorl-hns.2010.53.4.215.

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32

Cohn, J. D. "Power spectrum and correlation function errors: Poisson vs. Gaussian shot noise." New Astronomy 11, no. 4 (January 2006): 226–39. http://dx.doi.org/10.1016/j.newast.2005.08.002.

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33

Campillo, Michel, Laurent Stehly, Nikolai Shapiro, and Mike Ritzwoller. "Correlation in ambient seismic noise and the reconstruction of Green function." Journal of the Acoustical Society of America 117, no. 4 (April 2005): 2393. http://dx.doi.org/10.1121/1.4785865.

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34

Padoan, Paolo, Erik W. Rosolowsky, and Alyssa A. Goodman. "The Effects of Noise and Sampling on the Spectral Correlation Function." Astrophysical Journal 547, no. 2 (February 2001): 862–71. http://dx.doi.org/10.1086/318378.

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35

Zhang, Wei, Jin Fang Cheng, and Jie Xu. "Suppression of Single Vector Hydrophone Coherent-Noise Based on the Cross-SCF." Advanced Materials Research 588-589 (November 2012): 948–52. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.948.

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At present the cross-correlation processing can only suppress the isotropic noise by vector hydrophone sound pressure and vibration velocity combined. The coherent composition of the actual ambient noise makes the detection ability of cross-correlation spectrum reduced. Use XWVD theory, proposed a cross symmetry-correlation function (Cross-SCF). Analysis of simulation data under different SNR and Different nature noise combination proving that the noise suppression Performance of suggested Cross-SCF has nothing to do with noise properties, and compared with the cross-correlation processing have indeed better than coherent noise suppression ability.

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36

Wang, G., T. L. Rhodes, and W. A. Peebles. "Analysis method for calculating radial correlation length of electron temperature turbulence from correlation electron cyclotron emission radiometer." Review of Scientific Instruments 93, no. 11 (November 1, 2022): 113511. http://dx.doi.org/10.1063/5.0101680.

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The radial correlation length ( L r) is one of the essential quantities to measure in order to more fully characterize and understand turbulence and anomalous transport in magnetic fusion plasmas. The analysis method for calculating L r of electron temperature (Te) turbulence from correlation electron cyclotron emission (correlation ECE or CECE) radiometer measurements has not been fully developed partly due to the fact that the turbulent electron temperature fluctuations are generally imbedded in much larger amplitude thermal noise, which leads to a greatly reduced cross correlation coefficient ( ϱ) between two spatially separated ECE signals. This work finds that this ϱ reduction factor due to thermal noise is a function of the local relative temperature fluctuation power and CECE system bandwidths of intermediate and video frequencies, independent of radial separations. This indicates that under the approximation of constant relative temperature fluctuation power for a small radial range of local CECE measurements, the original shape of ϱ as a function of radial separation without thermal noise is preserved in the CECE data with thermal noise present. For Te turbulence with a Gaussian radial wavenumber spectrum, a fit function using the product of Gaussian and sinusoidal functions is derived for calculating L r. This analysis method has been numerically tested using simulated ECE radiometer data over a range of parameters. Using this method, the experimental temperature turbulence correlation length L r in a DIII-D L-mode plasma is found to be ∼10 times the local ion gyroradius.

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37

NG, KIN-WANG, and GUO-CHIN LIU. "CORRELATION FUNCTIONS OF CMB ANISOTROPY AND POLARIZATION." International Journal of Modern Physics D 08, no. 01 (February 1999): 61–83. http://dx.doi.org/10.1142/s0218271899000079.

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We give a full analysis of the auto- and cross-correlations between the Stokes parameters of the cosmic microwave background. In particular, we derive the windowing function for an antenna with Gaussian response in polarization experiment, and construct correlation function estimators corrected for instrumental noise. They are applied to calculate the signal to noise ratios for future anisotropy and polarization measurements. While the small-angular-scale anisotropy-polarization correlation would be likely detected by the MAP satellite, the detection of electric and magnetic polarization would require higher experimental sensitivity. For large-angular-scale measurements such as the being planned SPOrt/ISS, the expected signal to noise ratio for polarization is greater than one only for reionized models with high reionization redshifts, and the ratio is less for anisotropy-polarization correlation. Correlation and covariance matrices for likelihood analyses of ground-based and satellite data are also given.

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38

Li, Jiangtao, Richard L. Weaver, John Y. Yoritomo, and Xiaodong Song. "Application of temporal reweighting to ambient noise cross-correlation for improved seismic Green's function." Geophysical Journal International 221, no. 1 (January 6, 2020): 265–72. http://dx.doi.org/10.1093/gji/ggaa001.

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SUMMARY Due to the partly diffuse character of ambient noise, the retrieval of amplitude information and attenuation from noise cross-correlations has been difficult. Here, we apply the temporal reweighting method proposed by Weaver & Yoritomo to seismic data from the USArray in the central-midwest US. The results show considerable improvements in retrieved Green's functions in both symmetry and causality. The reweighting is able to make the effective incident noise field more isotropic (though not yet truly isotropic). It produces more robust amplitude measurements and also makes both the causal and anticausal parts usable. This suggests that it could be widely applicable for retrieval of Green's functions from ambient noise for attenuation study. The results also suggest an alternative measure of signal-to-noise ratio that complements the conventional one.

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39

Taylor, Sheldon, Owen Sharpe, and Jiju Peethambaran. "Prime gradient noise." Computational Visual Media 7, no. 3 (February 27, 2021): 349–62. http://dx.doi.org/10.1007/s41095-021-0206-z.

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AbstractProcedural noise functions are fundamental tools in computer graphics used for synthesizing virtual geometry and texture patterns. Ideally, a procedural noise function should be compact, aperiodic, parameterized, and randomly accessible. Traditional lattice noise functions such as Perlin noise, however, exhibit periodicity due to the axial correlation induced while hashing the lattice vertices to the gradients. In this paper, we introduce a parameterized lattice noise called prime gradient noise (PGN) that minimizes discernible periodicity in the noise while enhancing the algorithmic efficiency. PGN utilizes prime gradients, a set of random unit vectors constructed from subsets of prime numbers plotted in polar coordinate system. To map axial indices of lattice vertices to prime gradients, PGN employs Szudzik pairing, a bijection F : ℕ2 → ℕ. Compositions of Szudzik pairing functions are used in higher dimensions. At the core of PGN is the ability to parameterize noise generation though prime sequence offsetting which facilitates the creation of fractal noise with varying levels of heterogeneity ranging from homogeneous to hybrid multifractals. A comparative spectral analysis of the proposed noise with other noises including lattice noises show that PGN significantly reduces axial correlation and hence, periodicity in the noise texture. We demonstrate the utility of the proposed noise function with several examples in procedural modeling, parameterized pattern synthesis, and solid texturing.

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40

Fa, Kwok Sau. "Fractional oscillator noise and its applications." International Journal of Modern Physics B 34, no. 26 (September 18, 2020): 2050234. http://dx.doi.org/10.1142/s0217979220502343.

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It is shown that a fractional oscillator (FO) noise, which is a generalization of the ordinary overdamped linear oscillator driven by the white noise may be ‘applied to diverse systems; its stationary correlation function presents power-law-like function, exponential-like function, exponential function, and oscillatory decays. The model may be employed to describe the fluctuation of the distance between a fluorescein–tyrosine pair within a single protein complex and the internal dynamics of a lysozyme molecule in solution. It also has the possibility of describing a Brownian particle in an oscillatory viscoelastic shear flow.

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41

Li, Li, and Mingyan He. "A Robust DOA Estimation Based on Sigmoid Transform in Alpha Stable Noise Environment." MATEC Web of Conferences 173 (2018): 02006. http://dx.doi.org/10.1051/matecconf/201817302006.

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To suppress alpha-stable noise and co-channel interference, this paper defines a novel cyclic correlation function, and proposes a new MUSIC algorithm based on sigmoid cyclic correlation function. Furthermore, the proposed algorithm (SCC-MUSIC) is applied to estimate direction of arrival (DOA) in alpha stable distribution noise. Simulation results demonstrate that the proposed SCC-MUSIC can get a better performance than several existing algorithms especially in the highly impulsive noise environments.

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42

Воловач, В. И. "Mathematical modeling of the correlation function and the energy spectra of the noise modulation function." Informacionno-technologicheskij vestnik, no. 1(27) (March 15, 2021): 77–92. http://dx.doi.org/10.21499/2409-1650-2021-27-1-77-92.

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Рассмотрены и проанализированы вопросы, связанные с математическим моделированием корреляционных функций и энергетических спектров функции помеховой модуляции. Показано, что при воздействии на сигнал узкополосной мультипликативной помехи в энергетическом спектре функции помеховой модуляции присутствует дискретная составляющая, мощность которой зависит от глубины фазовых искажений. При импульсно-флуктуационной модулирующей помехе с детерминированным тактовым интервалом энергетический спектр функции помеховой модуляции представляет собой сумму непрерывной и дискретной частей. The issues related to mathematical modeling of correlation functions and energy spectra of the noise modulation function are considered and analyzed. It is shown that when a signal is affected by a narrow-band multiplicative interference, a discrete component is present in the energy spectrum of the interference modulation function, the power of which depends on the depth of the phase distortion. In the case of pulse-fluctuating modulating interference with a deterministic clock interval, the energy spectrum of the interference modulation function is the sum of the continuous and discrete parts.

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43

Sabra, Karim G., Philippe Roux, and W. A. Kuperman. "Emergence rate of the time-domain Green’s function from the ambient noise cross-correlation function." Journal of the Acoustical Society of America 118, no. 6 (December 2005): 3524–31. http://dx.doi.org/10.1121/1.2109059.

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44

Sabra, Karim, Philippe Roux, Peter Gerstoft, and W. A. Kuperman. "Emergence rate of the time‐domain Green’s function from the ambient noise cross‐correlation function." Journal of the Acoustical Society of America 118, no. 3 (September 2005): 1845–46. http://dx.doi.org/10.1121/1.4809069.

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45

Badillo, Inari, and Joaquín Portilla. "Experimental Study of AM and PM Noise in Cascaded Amplifiers." Electronics 11, no. 3 (February 5, 2022): 470. http://dx.doi.org/10.3390/electronics11030470.

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An experimental study of amplitude modulation (AM) and phase modulation (PM) noise spectra in cascaded amplifiers was carried out as a function of the number of amplification stages and the input power. Flicker and white noise contributions were determined, as well as effective noise figure (NF) from AM and PM noise spectra from small-signal to large-signal regimes. Simultaneous measurements of AM and PM noise were performed, and associated correlation was measured as a function of the offset frequency from the carrier. Measurements exhibited, in general, quite low AM–PM correlation levels both in the flicker and white noise parts of the spectrum. In some particular amplifier configurations, however, measurements showed some peaks in the correlation at some specific input power levels in the transition zone, from a quasi-linear to strong compression. The results show that the effective noise figure decreases with the number of stages for a given carrier output power level.

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46

Dou, Yuzi, and Sen Li. "Kernel Function-Based Ambiguity Function and Its Application on DOA Estimation in Impulsive Noise." Sensors 22, no. 18 (September 15, 2022): 6996. http://dx.doi.org/10.3390/s22186996.

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To solve the problem that the traditional ambiguity function cannot well reflect the time-frequency distribution characteristics of linear frequency modulated (LFM) signals due to the presence of impulsive noise, two robust ambiguity functions: correntropy-based ambiguity function (CRAF) and fractional lower order correntropy-based ambiguity function (FLOCRAF) are defined based on the feature that correntropy kernel function can effectively suppress impulsive noise. Then these two robust ambiguity functions are used to estimate the direction of arrival (DOA) of narrowband LFM signal under an impulsive noise environment. Instead of the covariance matrix used in the ESPRIT algorithm by the spatial CRAF matrix and FLOCRAF matrix, the CRAF-ESPRIT and FLOCRAF-ESPRIT algorithms are proposed. Computer simulation results show that compared with the algorithms only using ambiguity function and the algorithms only using the correntropy kernel function-based correlation, the proposed algorithms using ambiguity function based on correntropy kernel function have good performance in terms of probability of resolution and estimation accuracy under various circumstances. Especially, the performance of the FLOCRAF-ESPRIT algorithm is better than the CRAF-ESPRIT algorithm in the environment of low generalized signal-to-noise ratio and strong impulsive noise.

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47

ZHAO, G. H., Y. L. XIANG, and D. C. MEI. "EFFECTS OF CORRELATION BETWEEN REAL AND IMAGINARY PARTS OF THE QUADRATIC PUMP NOISE ON THE INTENSITY FLUCTUATION OF A SINGLE-MODE LASER SYSTEM." Modern Physics Letters B 23, no. 02 (January 20, 2009): 155–61. http://dx.doi.org/10.1142/s0217984909017856.

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The effects of the correlations between real and imaginary parts of the quadratic pump noise on the normalized intensity correlation function and the associated relaxation time of a single-mode laser model were investigated. The expressions of the intensity correlation function C(s) and the relaxation time Tc were derived. Based on numerical computations, we found that Tc monotonously increases as the strength λp of correlation between the real and imaginary parts of quadratic pump noise increases and the larger λp value is, the slower C(s) decays. The presence of correlations between the real and imaginary parts of the quadratic pump noise causes the intensity fluctuation to increase.

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48

Miles, Jeffrey Hilton. "Separating Direct and Indirect Turbofan Engine Combustion Noise Using the Correlation Function." Journal of Propulsion and Power 26, no. 5 (September 2010): 1144–52. http://dx.doi.org/10.2514/1.48908.

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49

Farah, George N., and Benjamin Lindner. "Exponentially distributed noise—its correlation function and its effect on nonlinear dynamics." Journal of Physics A: Mathematical and Theoretical 54, no. 3 (December 31, 2020): 035003. http://dx.doi.org/10.1088/1751-8121/abd2fd.

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50

Becker, V., and H. K. Janssen. "Current-current correlation function in a driven diffusive system with nonconserving noise." Physical Review E 50, no. 2 (August 1, 1994): 1114–22. http://dx.doi.org/10.1103/physreve.50.1114.

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