Relevant bibliographies by topics / Recursive digital filters

Academic literature on the topic 'Recursive digital filters'

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Published: 6 September 2023

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Journal articles on the topic "Recursive digital filters"

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Siwczyński, M., A. Drwal, and S. Żaba. "The digital function filters – algorithms and applications." Bulletin of the Polish Academy of Sciences: Technical Sciences 61, no. 2 (June 1, 2013): 371–77. http://dx.doi.org/10.2478/bpasts-2013-0036.

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Abstract The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.
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Porsani, Milton J., and Bjørn Ursin. "Direct multichannel predictive deconvolution." GEOPHYSICS 72, no. 2 (March 2007): H11—H27. http://dx.doi.org/10.1190/1.2432260.

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The Levinson principle generally can be used to compute recursively the solution of linear equations. It can also be used to update the error terms directly. This is used to do single-channel deconvolution directly on seismic data without computing or applying a digital filter. Multichannel predictive deconvolution is used for seismic multiple attenuation. In a standard procedure, the prediction-error filter matrices are computed with a Levinson recursive algorithm, using a covariance matrix of the input data. The filtered output is the prediction errors or the nonpredictable part of the data. Starting with the classical Levinson recursion,wehave derived new algorithms for direct recursive calculationof the prediction errors without computing the data covariance-matrix or computing the prediction-error filters. One algorithm generates recursively the one-step forward and backward predic-tion errors and the L-step forward prediction error, computing only the filter matrices with the highest index. A numerically more stable algorithm uses reduced QR decomposition or singular-value decomposition (SVD) in a direct recursive computation of the prediction errors without computing any filter matrix. The new, stable, predictive algorithms require more arithmetic opera-tions in the computer, but the computer programs and data flow are much simpler than for standard predictive deconvolution.
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Kaplun, Dmitry, Denis Butusov, Valerii Ostrovskii, Alexander Veligosha, and Vyacheslav Gulvanskii. "Optimization of the FIR Filter Structure in Finite Residue Field Algebra." Electronics 7, no. 12 (December 2, 2018): 372. http://dx.doi.org/10.3390/electronics7120372.

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This paper introduces a method for optimizing non-recursive filtering algorithms. A mathematical model of a non-recursive digital filter is proposed and a performance estimation is given. A method for optimizing the structural implementation of the modular digital filter is described. The essence of the optimization is that by using the property of the residue ring and the properties of the symmetric impulse response of the filter, it is possible to obtain a filter having almost a half the length of the impulse response compared to the traditional modular filter. A difference equation is given by calculating the output sample of modules p1 … pn in the modified modular digital filter. The performance of the modular filters was compared with the performance of positional non-recursive filters implemented on a digital signal processor. An example of the estimation of the hardware costs is shown to be required for implementing a modular digital filter with a modified structure. This paper substantiates the expediency of applying the natural redundancy of finite field algebra codes on the example of the possibility to reduce hardware costs by a factor of two. It is demonstrated that the accuracy of data processing in the modular digital filter is higher than the accuracy achieved with the implementation of filters on digital processors. The accuracy advantage of the proposed approach is shown experimentally by the construction of the frequency response of the non-recursive low-pass filters.
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Deng, Tian-Bo. "Generalized Stability-Triangle for Guaranteeing the Stability-Margin of the Second-Order Digital Filter." Journal of Circuits, Systems and Computers 25, no. 08 (May 17, 2016): 1650094. http://dx.doi.org/10.1142/s0218126616500948.

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In the design of recursive digital filters, the stability of the recursive digital filters must be guaranteed. Furthermore, it is desirable to add a certain amount of margin to the stability so as to avoid the violation of stability due to some uncertain perturbations of the filter coefficients. This paper extends the well-known stability-triangle of the second-order digital filter into more general cases, which results in dented stability-triangles and generalized stability-triangle. The generalized stability-triangle can be viewed as a special case of the dented stability-triangles if the two upper bounds on the radii of the two poles are the same, which is a generalized version of the existing conventional stability-triangle and can guarantee the radii of the two poles of the second-order recursive digital filter below some prescribed upper bound. That is, it is able to provide a prescribed stability-margin in terms of the upper bound of the pole radii. As a result, the generalized stability-triangle increases the flexibility for guaranteeing a prescribed stability-margin. Since the generalized stability-triangle is parameterized by using the upper bound of pole radii, i.e., the stability-margin is parameterized as a function of the upper bound, the proposed generalized stability-triangle facilitates the stability-margin guarantee in the design of the second-order as well as high-order recursive digital filters.
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Çetin, A. Enis, and Rashid Ansari. "Digital interpolation beamforming using recursive filters." Journal of the Acoustical Society of America 85, no. 1 (January 1989): 493–95. http://dx.doi.org/10.1121/1.397701.

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NIKOLIC, SASA V., and VIDOSAV S. STOJANOVIC. "Transitional Butterworth-Chebyshev recursive digital filters." International Journal of Electronics 80, no. 1 (January 1996): 13–20. http://dx.doi.org/10.1080/002072196137552.

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Murthy, H., Daka Reddy, and P. Reddy. "Stabilization of Multidimensional Recursive Digital Filters." IEEE Transactions on Geoscience and Remote Sensing GE-23, no. 2 (March 1985): 158–63. http://dx.doi.org/10.1109/tgrs.1985.289413.

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Stancic, Goran, and Sasa Nikolic. "Design of narrow stopband recursive digital filter." Facta universitatis - series: Electronics and Energetics 24, no. 1 (2011): 119–30. http://dx.doi.org/10.2298/fuee1101119s.

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The procedure for design of narrow stopband recursive digital filter realized through parallel connections of two allpass sub-filters is described in this paper. This solution also allows realization of complementary filter, using only one additional adder, and exhibit low sensitivity on coefficients quantization. The method is based on phase approximation of allpass sub-filter. The procedure is very efficient and solution can be obtained within only a few iterations even for large filter order n. Every stopband provides two more equations, one at notch frequency and the other at passband boundary. It is not possible to control attenuation at both passband boundaries, but described procedure provides that achieved attenuations are less or equal to prescribed values. Using this algorithm full control of passband edges is obtained comparing with existing methods where it is not possible.
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Deng, Tian-Bo. "Stability-Guaranteed Two-Phase Design of Odd-Order Variable-Magnitude Digital Filters." Journal of Circuits, Systems and Computers 26, no. 02 (November 3, 2016): 1750033. http://dx.doi.org/10.1142/s0218126617500335.

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Guaranteeing the stability is one of the most critical issues in designing a variable recursive digital filter. In this paper, we first present an odd-order recursive variable model (transfer function) that is used for designing an odd-order variable-magnitude (VM) digital filter, and then we replace the original coefficients of the denominator of the odd-order transfer function with a set of new parameters. These new parameters can ensure that they can take arbitrary values without incurring instability of the designed odd-order VM filter. To make the VM filter coefficients variable, we find all the VM filter coefficients as polynomial functions of the tuning parameter, which includes two phases. The first phase designs a set of recursive digital filters with fixed coefficients (constant filters), and the second phase utilizes a curve-fitting scheme to represent each coefficient as a polynomial function. As a result, the VM filter coefficients become variable, and the proposed parameter-substitution-based denominator coefficients ensure the filter stability. This is the most important contribution of the parameter-substitution-based design scheme. This paper uses the fifth-order demonstrative example to verify the stability guarantee as well as the design accuracy of the obtained the fifth-order VM filter.
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Feng, Z., and R. Unbehauen. "Synthesis of recursive digital filters by state feedback of non-recursive cascaded lattice filters." International Journal of Circuit Theory and Applications 14, no. 2 (April 1986): 147–52. http://dx.doi.org/10.1002/cta.4490140204.

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Dissertations / Theses on the topic "Recursive digital filters"

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Price, Marc Royston. "Hybrid structures for high order recursive filters." Thesis, King's College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339120.

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Davati, Soheil. "VLSI implementation of recursive digital notch filter." Ohio : Ohio University, 1986. http://www.ohiolink.edu/etd/view.cgi?ohiou1183128831.

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Katsianos, Themis G. "Digital recursive filters : a tutorial for filter designers with examples implemented in Csound and supercollider." Thesis, McGill University, 1997. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=28283.

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Filters constitute an essential tool for manipulating the spectral content of a signal. While there is a plethora of filtering tools, both in the hardware and software domain, the majority of them are geared towards engineers and scientists, rather than sound designers and electroacoustic composers. The "common-practice" approach is to consider filters as post-production tools. This can be restrictive if filters are to be used as artistic tools, dynamically involved in the shaping of the sound. This thesis was written with this approach in mind its aim is (a) to provide a survey of the various digital recursive filters, enabling a filter designer to choose the one that suits his needs, (b) to teach filter designers, such as electroacoustic composers and sound designers how to calculate digital filter coefficients, and (c) implement filter algorithms using the familiar syntax of computer music languages such as Csound and SuperCollider .
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SHENG, CHANG PI. "ANALYSIS AND SYNTHESIS OF LIMIT CYCLE FREE RECURSIVE DIGITAL FILTERS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1990. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=14161@1.

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Neste trabalho é desenvolvido um método de análise de ciclo limite devido à quantização, à entrada zero, para redes operando com aritmética em ponto flutuante. Condições de inexistência de ciclo limite são facilmente obtidas via cálculo computacional. O método de análise se aplica a redes genéricas de qualquer ordem. É desenvolvido, em seguida, um método de síntese de redes operando com aritmética em ponto fixo, que são imunes a ciclo limite devido à quantização, à entrada zero, utilizando para isso o conceito de redes estruturalmente passivas. As redes assim sintetizadas apresentam sub-redes estruturalmente LBR ou BR na sua malha de realimentação. São as redes de segunda ordem, sintetizadas pelo método proposto. É provado que algumas dessas redes são também imunes a ciclo limite devido a overflow, à entrada zero e a resposta forçada.
This thesis presents a method for analysis of zero-input limit cycles due to quantization, in digital filters realized with floating point arithmetic. Conditions for absence of limit cycles are easily derived by computational calculus. The method of analysis is applicable to generic structures of any order. Following this, a method is presented a method for the synthesis of digital filters realized with fixed point arithmetic, that are free from zero-input limit cycles due to quantization, using the concept of structurally passive networks. The structures synthetized present sub-filters structurally LBR or BR in the feedback loop. Second order structures are synthetized and studied. It is proved that some of these stuctures are also free from zero-input limit cycles due to overflow and stable to forced response.
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Mohsén, Mikael. "Implementation and Evaluation of Single Filter Frequency Masking Narrow-Band High-Speed Recursive Digital Filters." Thesis, Linköping University, Department of Electrical Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-1522.

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In this thesis two versions of a single filter frequency masking narrow-band high-speed recursive digital filter structure, proposed in [1], have been implemented and evaluated considering the maximal clock frequency, the maximal sample frequency and the power consumption. The structures were compared to a conventional filter structure, that was also implemented. The aim was to see if the proposed structure had some benefits when implemented and synthesized, not only in theory. For the synthesis standard cells from AMS csx 0.35 mm CMOS technology were used.

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Katsianos, Themis G. "Digital recursive filters, a tutorial for filter designers with examples implemented in Csound and SuperCollider." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/mq43893.pdf.

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Doheny, David A. "Real Time Digital Signal Processing Adaptive Filters for Correlated Noise Reduction in Ring Laser Gyro Inertial Systems." [Tampa, Fla.] : University of South Florida, 2004. http://purl.fcla.edu/fcla/etd/SFE0000306.

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Trebien, Fernando. "An efficient GPU-based implementation of recursive linear filters and its application to realistic real-time re-synthesis for interactive virtual worlds." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2009. http://hdl.handle.net/10183/18251.

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Muitos pesquisadores têm se interessado em explorar o vasto poder computacional das recentes unidades de processamento gráfico (GPUs) em aplicações fora do domínio gráfico. Essa tendência ao desenvolvimento de propósitos gerais com a GPU (GPGPU) foi intensificada com a produção de APIs não-gráficas, tais como a Compute Unified Device Architecture (CUDA), da NVIDIA. Com elas, estudou-se a solução na GPU de muitos problemas de processamento de sinal 2D e 3D envolvendo álgebra linear e equações diferenciais parciais, mas pouca atenção tem sido dada ao processamento de sinais 1D, que também podem exigir recursos computacionais significativos. Já havia sido demonstrado que a GPU pode ser usada para processamento de sinais em tempo-real, mas alguns processos não se adequavam bem à arquitetura da GPU. Neste trabalho, apresento uma nova técnica para implementar um filtro digital linear recursivo usando a GPU. Até onde eu sei, a solução aqui apresentada é a primeira na literatura. Uma comparação entre esta abordagem e uma implementação equivalente baseada na CPU demonstra que, quando usada em um sistema de processamento de áudio em temporeal, esta técnica permite o processamento de duas a quatro vezes mais coeficientes do que era possível anteriormente. A técnica também elimina a necessidade de processar o filtro na CPU - evitando transferências de memória adicionais entre CPU e GPU - quando se deseja usar o filtro junto a outros processos, tais como síntese de som. A recursividade estabelecida pela equação do filtro torna difícil obter uma implementação eficiente em uma arquitetura paralela como a da GPU. Já que cada amostra de saída é computada em paralelo, os valores necessários de amostras de saída anteriores não estão disponíveis no momento do cômputo. Poder-se-ia forçar a GPU a executar o filtro sequencialmente usando sincronização, mas isso seria um uso ineficiente da GPU. Este problema foi resolvido desdobrando-se a equação e "trocando-se" as dependências de amostras próximas à saída atual por outras precedentes, assim exigindo apenas o armazenamento de um certo número de amostras de saída. A equação resultante contém convoluções que então são eficientemente computadas usando a FFT. A implementação da técnica é geral e funciona para qualquer filtro recursivo linear invariante no tempo. Para demonstrar sua relevância, construímos um filtro LPC para sintetizar em tempo-real sons realísticos de colisões de objetos feitos de diferentes materiais, tais como vidro, plástico e madeira. Os sons podem ser parametrizados por material dos objetos, velocidade e ângulo das colisões. Apesar de flexível, esta abordagem usa pouca memória, exigindo apenas alguns coeficientes para representar a resposta ao impulso do filtro para cada material. Isso torna esta abordagem uma alternativa atraente frente às técnicas tradicionais baseadas em CPU que apenas realizam a reprodução de sons gravados.
Many researchers have been interested in exploring the vast computational power of recent graphics processing units (GPUs) in applications outside the graphics domain. This trend towards General-Purpose GPU (GPGPU) development has been intensified with the release of non-graphics APIs for GPU programming, such as NVIDIA's Compute Unified Device Architecture (CUDA). With them, the GPU has been widely studied for solving many 2D and 3D signal processing problems involving linear algebra and partial differential equations, but little attention has been given to 1D signal processing, which may demand significant computational resources likewise. It has been previously demonstrated that the GPU can be used for real-time signal processing, but several processes did not fit the GPU architecture well. In this work, a new technique for implementing a digital recursive linear filter using the GPU is presented. To the best of my knowledge, the solution presented here is the first in the literature. A comparison between this approach and an equivalent CPU-based implementation demonstrates that, when used in a real-time audio processing system, this technique supports processing of two to four times more coefficients than it was possible previously. The technique also eliminates the necessity of processing the filter on the CPU - avoiding additional memory transfers between CPU and GPU - when one wishes to use the filter in conjunction with other processes, such as sound synthesis. The recursivity established by the filter equation makes it difficult to obtain an efficient implementation on a parallel architecture like the GPU. Since every output sample is computed in parallel, the necessary values of previous output samples are unavailable at the time the computation takes place. One could force the GPU to execute the filter sequentially using synchronization, but this would be a very inefficient use of GPU resources. This problem is solved by unrolling the equation and "trading" dependences on samples close to the current output by other preceding ones, thus requiring only the storage of a limited number of previous output samples. The resulting equation contains convolutions which are then efficiently computed using the FFT. The proposed technique's implementation is general and works for any time-invariant recursive linear filter. To demonstrate its relevance, an LPC filter is designed to synthesize in real-time realistic sounds of collisions between objects made of different materials, such as glass, plastic, and wood. The synthesized sounds can be parameterized by the objects' materials, velocities and collision angles. Despite its flexibility, this approach uses very little memory, requiring only a few coefficients to represent the impulse response for the filter of each material. This turns this approach into an attractive alternative to traditional CPU-based techniques that use playback of pre-recorded sounds.
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Jangsri, Venus. "Infinite impulse response notch filter." Thesis, Monterey, California. Naval Postgraduate School, 1988. http://hdl.handle.net/10945/23269.

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A pipeline technique by Loomis and Sinha has been applied to the design of recursive digital filters. Recursive digital filters operating at hitherto impossibly high rates can be designed by this technique. An alternate technique by R. Gnanasekaran allows high speed implementation using the state-space structure directly. High throughput is also achieved by use of pipelined multiply-add modules. The actual hardware complexity will depend upon the number of pipeline stages. These techniques are used for the design of the I IR notch filter and finally, a comparison of the performance and complexity of these two techniques is presented.
http://archive.org/details/infiniteimpulser00jang
Lieutenant, Royal Thai Navy
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Sabbatini, Junior Narcizo. "Um sistema para o projeto de filtros digitais recursivos descritos por variaveis de estado." [s.n.], 1990. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261950.

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Orientador: Amauri Lopes
Dissertação (mestrado) - universidade Estadual de Campinas, Faculdade de Engenharia Eletrica
Made available in DSpace on 2018-07-13T21:53:22Z (GMT). No. of bitstreams: 1 SabbatiniJunior_Narcizo_M.pdf: 6859144 bytes, checksum: 9530ae5fecdd6f6b155120f4f29e4b7e (MD5) Previous issue date: 1990
Resumo: Este trabalho descreve os aspectos teóricos e práticos envolvidos na elaboração do programa de computador FOREST, que sintetiza e analisa filtros digitais recursivos. São sintetizados filtros passa-baixa, passa-alta, passa faixa e corta-faixa, utilizando-se as aproximações de Butterworth, Chebychev e elíptica. Os efeitos não lineares advindos da utilização de registros de comprimento finito para a representação de coeficientes e variáveis são analisados em detalhe. Apresenta-se a teoria de otimização dos filtros digitais com relação ao ruído de quantização do sinal, baseada na descrição por variáveis de estado, e o programa incorpora essa teoria gerando filtros descritos por variáveis de estado com reduzidos efeitos de quantização
Abstract: Not informed.
Mestrado
Mestre em Engenharia Elétrica
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Books on the topic "Recursive digital filters"

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Chung, Jin-Gyun, and Keshab K. Parhi. Pipelined Lattice and Wave Digital Recursive Filters. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1307-6.

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Chung, Jin-Gyun. Pipelined lattice and wave digital recursive filters. Boston: Kluwer Academic Publishers, 1996.

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Chung, Jin-Gyun. Pipelined Lattice and Wave Digital Recursive Filters. Boston, MA: Springer US, 1996.

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Valcartier, Canada Defence Research Establishment. Acceleration-Invariant Approximation Method For Recursive Digital Filters. S.l: s.n, 1985.

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Smith, Mark J. T. Recursive time-varying filter banks for subband image coding. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Smith, Mark J. T. Recursive time-varying filter banks for subband image coding. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Smith, Mark J. T. Recursive time-varying filter banks for subband image coding. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Bandyopadhyay, A. Initialization experiments over Indian region with a limited area model using recursive digital filters. Pune: Indian Institute of Tropical Meteorology, 2004.

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Ernst, Thomas. Adaptive Detektoren für die Datenübertragung über rekursive Kanäle. Konstanz: Hartung-Gorre, 1996.

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Book chapters on the topic "Recursive digital filters"

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King, Robert, Majid Ahmadi, Raouf Gorgui-Naguib, Alan Kwabwe, and Mahmood Azimi-Sadjadi. "Recursive Filters." In Digital Filtering in One and Two Dimensions, 119–96. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4899-0918-3_4.

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Terrell, Trevor J. "Design of Recursive Digital Filters." In Introduction to Digital Filters, 52–100. London: Palgrave Macmillan UK, 1988. http://dx.doi.org/10.1007/978-1-349-19345-5_2.

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Terrell, Trevor J. "Design of Non-recursive Digital Filters." In Introduction to Digital Filters, 101–23. London: Palgrave Macmillan UK, 1988. http://dx.doi.org/10.1007/978-1-349-19345-5_3.

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Buttkus, Burkhard. "Synthesis of Recursive Digital Filters." In Spectral Analysis and Filter Theory in Applied Geophysics, 379–403. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57016-2_19.

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Padmanabhan, Mukund, Ken Martin, and Gábor Péceli. "Computation of Time-Recursive Transforms." In Feedback-Based Orthogonal Digital Filters, 59–110. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1305-2_3.

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Chung, Jin-Gyun, and Keshab K. Parhi. "Pipelining Direct Form Recursive Digital Filters." In The Kluwer International Series in Engineering and Computer Science, 21–47. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1307-6_3.

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Phillips, Braden J., Neil Burgess, and Ken V. Lever. "Regularisation Procedures for Iterated Recursive Digital Filters." In Digital Signal Processing for Communication Systems, 217–24. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6119-4_24.

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Chung, Jin-Gyun, and Keshab K. Parhi. "Roundoff Noise in Pipelined Recursive Digital Filters." In The Kluwer International Series in Engineering and Computer Science, 49–77. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1307-6_4.

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Vergis, Anastasios, and Vassilios Verykios. "On the testability of purely recursive digital filters." In PARLE'94 Parallel Architectures and Languages Europe, 85–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58184-7_92.

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Kochegurova, Elena, Ivan Khozhaev, and Tatyana Ezangina. "Design of Recursive Digital Filters with Penalized Spline Method." In Computational Collective Intelligence, 3–12. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98446-9_1.

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Conference papers on the topic "Recursive digital filters"

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Stamenkovic, Negovan, and Vidosav Stojanovic. "Transitional Butterworth-Thiran recursive digital filters." In 2012 20th Telecommunications Forum Telfor (TELFOR). IEEE, 2012. http://dx.doi.org/10.1109/telfor.2012.6419324.

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Kadriu, Edona, and Lufti Bina. "Design of recursive digital filters (IIR)." In University for Business and Technology International Conference. Pristina, Kosovo: University for Business and Technology, 2018. http://dx.doi.org/10.33107/ubt-ic.2018.336.

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Gilmanshin, Iskander, Ramil Shaimukhametov, and Vladimir Strekalov. "Digital Recursive Filters for Building Thermal Modelling." In 2018 IEEE East-West Design & Test Symposium (EWDTS). IEEE, 2018. http://dx.doi.org/10.1109/ewdts.2018.8524702.

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Holdcroft, D. "Comparative study of recursive digital filters using z and operators." In IEE Sixteenth Saraga Colloquium on Digital and Analogue Filters and Filtering Systems. IEE, 1996. http://dx.doi.org/10.1049/ic:19961270.

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Musa, M. "Optimisation of complex recursive digital filters operating in transient mode." In IEE 15th SARAGA Colloquium on Digital and Analogue Filters and Filtering Systems. IEE, 1995. http://dx.doi.org/10.1049/ic:19951460.

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Musa, M. A. "An equivalent non-recursive filter for a complex recursive filter with its associated non-zero frequency initialisation processor." In IEE Sixteenth Saraga Colloquium on Digital and Analogue Filters and Filtering Systems. IEE, 1996. http://dx.doi.org/10.1049/ic:19961268.

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Yli-Kaakinen, Juha, and Tapio Saramaki. "Efficient Recursive Digital Filters with Variable Magnitude Characteristics." In Proceedings of the 7th Nordic Signal Processing Symposium - NORSIG 2006. IEEE, 2006. http://dx.doi.org/10.1109/norsig.2006.275268.

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Zivaljevic, Dragana U., and Sasa V. Nikolic. "Design of Recursive Digital Filters for Subband Coding." In 2018 26th Telecommunications Forum (TELFOR). IEEE, 2018. http://dx.doi.org/10.1109/telfor.2018.8611855.

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Milic, Ljiljana D., and Jelena D. Certic. "Recursive digital filters and two-channel filter banks: Frequency-response masking approach." In TELSIKS 2009 - 2009 9th International Conference on Telecommunications in Modern Satellite, Cable, and Broadcasting Services. IEEE, 2009. http://dx.doi.org/10.1109/telsks.2009.5339431.

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Vargas, Ricardo A., and C. Sidney Burrus. "The direct design of recursive or IIR digital filters." In 2008 3rd International Symposium on Communications, Control and Signal Processing (ISCCSP). IEEE, 2008. http://dx.doi.org/10.1109/isccsp.2008.4537217.

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