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P.p. Vaidyanathan - One of the best experts on this subject based on the ideXlab platform.
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Efficient multiplier-less structures for Ramanujan Filter Banks
2017 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2017Co-Authors: P.p. Vaidyanathan, S. TennetiAbstract:Ramanujan Filter Banks (RFB) are useful to generate time-period plane plots which allow one to localize multiple periodic components in the time domain. For such applications, the RFB produces more satisfactory results compared to short time Fourier transforms and other conventional methods, as demonstrated in recent years. This paper introduces a novel multiplier-less, hence computationally very efficient, structure to implement Ramanujan Filter Banks, based on a new result connecting Ramanujan sums and natural periodic bases.
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Ramanujan Filter Banks for estimation and tracking of periodicities
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: S. Tenneti, P.p. VaidyanathanAbstract:We propose a new Filter-bank structure for the estimation and tracking of periodicities in time series data. These Filter-Banks are inspired from recent techniques on period estimation using high-dimensional dictionary representations for periodic signals. Apart from inheriting the numerous advantages of the dictionary based techniques over conventional period-estimation methods such as those using the DFT, the Filter-Banks proposed here expand the domain of problems that can be addressed to a much richer set. For instance, we can now characterize the behavior of signals whose periodic nature changes with time. This includes signals that are periodic only for a short duration and signals such as chirps. For such signals, we use a time vs period plane analogous to the traditional time vs frequency plane. We will show that such Filter Banks have a fundamental connection to Ramanujan Sums and the Ramanujan Periodicity Transform.
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Properties of Ramanujan Filter Banks
2015 23rd European Signal Processing Conference (EUSIPCO), 2015Co-Authors: P.p. Vaidyanathan, S. TennetiAbstract:This paper studies a class of Filter Banks called the Ramanujan Filter Banks which are based on Ramanujan-sums. It is shown that these Filter Banks have some important mathematical properties which allow them to reveal localized hidden periodicities in real-time data. These are also compared with traditional comb Filters which are sometimes used to identify periodicities. It is shown that non-adaptive comb Filters cannot in general reveal periodic components in signals unless they are restricted to be Ramanujan Filters. The paper also shows how Ramanujan Filter Banks can be used to generate time-period plane plots which track the presence of time varying, localized, periodic components.
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analog Filter Banks for sampling discretization polyphase form and role in compressive sensing
2013 IEEE Digital Signal Processing and Signal Processing Education Meeting (DSP SPE), 2013Co-Authors: P.p. VaidyanathanAbstract:Continuous-time signals arising in many applications can often be modeled as the outputs of analog synthesis-Filter Banks driven by discrete-time inputs di(n). Such a signal x(t) has a finite innovations rate, although it may not be bandlimited in general. In some applications it is necessary to sample such signals after Filtering with an analog sampling-Filter-bank, to recover the driving signals di(n): This sampling Filter bank is in general not unique, and the theory and design techniques for such analog Filter Banks are not as well developed as the large body of literature on digital Filter Banks. In this paper we show that the theoretical as well as design and implementation issues can be formulated in terms of digital Filter Banks, by taking advantage of the finite innovations rate of x(t): The rich body of knowledge on digital Filter Banks and polyphase forms can therefore be utilized and furthermore the optimization of the sampling Filter bank can be done on a more convenient platform. Applications of this development in the context of compressive sensing are also elaborated.
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the role of gtd in optimizing perfect reconstruction Filter Banks
IEEE Transactions on Signal Processing, 2012Co-Authors: Chingchih Weng, P.p. VaidyanathanAbstract:Filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications. In this paper we propose GTD (generalized triangular decomposition) Filter Banks as a subband coder for optimizing the theoretical coding gain. We focus on perfect reconstruction orthonormal GTD Filter Banks and biorthogonal GTD Filter Banks. We show that in both cases there are two fundamental properties in the optimal solutions, namely, total decorrelation and spectrum equalization. The optimal solutions can be obtained by performing the frequency dependent GTD on the Cholesky factor of the input power spectrum density matrices. We also show that in both theory and numerical simulations, the optimal GTD subband coders have superior performance than optimal traditional subband coders. In addition, the uniform bit loading scheme can, with no loss of optimality, be used in the optimal biorthogonal GTD coders, which solves the granularity problem in the conventional optimum bit loading formula. We then extend the use of GTD Filter Banks to wireless communication systems, where linear precoding and zero-forcing decision feedback equalization is used in frequency selective channels. We consider the quality of service (QoS) problem of minimizing the transmitted power subject to the bit error rate and total bit rate constraints. Optimal systems with orthonormal precoder and unconstrained precoder are both derived and shown to be related to the frequency dependent GTD of the channel frequency response.
Yuichi Tanaka - One of the best experts on this subject based on the ideXlab platform.
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two channel critically sampled graph Filter Banks with spectral domain sampling
IEEE Transactions on Signal Processing, 2019Co-Authors: Akie Sakiyama, Yuichi Tanaka, Kana Watanabe, Antonio OrtegaAbstract:We propose two-channel critically-sampled Filter Banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable properties: first, perfect reconstruction regardless of the characteristics of the underlying graphs and graph variation operators; and second, a symmetric structure; i.e., both analysis and synthesis Filter Banks are built using similar building blocks. Along with the structure of the Filter Banks, this paper also proves the general criterion for perfect reconstruction and theoretically shows that the vertex and spectral domain sampling coincide for a special case. The effectiveness of our approach is evaluated by comparing its performance in nonlinear approximation and denoising with various conventional graph transforms.
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critically sampled graph Filter Banks with polynomial Filters from regular domain Filter Banks
Signal Processing, 2017Co-Authors: D B H Tay, Yuichi Tanaka, Akie SakiyamaAbstract:Graph signal processing deals with the processing of signals defined on irregular domains and is an emerging area of research. Graph Filter Banks allow the wavelet transform to be extended for processing graph signals. Sakiyama and Tanaka (2015) 22 recently proposed a technique to convert linear-phase biorthogonal Filter Banks for regular domain signals to biorthogonal graph Filter Banks. Perfect reconstruction is preserved using the technique but the resulting spectral Filter functions are transcendental and not polynomial. Polynomial function Filters are desired for the localization property and implementation efficiency. In this work we present alternative techniques to perform the conversion. Perfect reconstruction is preserved with the proposed techniques and the resulting spectral Filters are polynomial functions. HighlightsWe design Filter Banks for signal defined over bipartite graphs.Spectral Filters are polynomials resulting in localization and efficient implementation.Technique is based on converting 1D regular domain Filter Banks.Perfect reconstruction is exactly preserved and spectral response shape is almost preserved.
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construction of undersampled graph Filter Banks via row subset selection
IEEE Global Conference on Signal and Information Processing, 2016Co-Authors: Akie Sakiyama, Yuichi TanakaAbstract:This paper introduces a construction method of M-channel under-sampled spectral graph Filter Banks. They can be applied to any kind of undirected graphs, use arbitrary critically sampled or oversampled analysis Filters, and obtain low redundancy, which is less than 1, regardless of the number of the analysis Filters. We formulate the construction problem as a row subset selection method of the transform matrix of the prototype (critically sampled or oversampled) Filter Banks. In the experiment, a graph signal on Minnesota Traffic Graph is decomposed to examine the performance of our spectral graph Filter Banks.
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spectral graph wavelets and Filter Banks with low approximation error
IEEE Transactions on Signal and Information Processing over Networks, 2016Co-Authors: Akie Sakiyama, Kana Watanabe, Yuichi TanakaAbstract:We propose Filter Banks in the graph spectral domain, where each Filter is defined by a sum of sinusoidal waves. The main advantages of these Filter Banks are that (a) they have low approximation errors even if a lower-order shifted Chebyshev polynomial approximation is used, (b) the upper bound of the error after the $p$ th order Chebyshev polynomial approximation can be calculated rigorously without complex calculations, and (c) their parameters can be efficiently obtained from any real-valued linear phase finite impulse response Filter Banks in regular signal processing. The proposed Filter bank has the same Filter characteristics as the corresponding classical Filter bank in the frequency domain and inherits the original properties, such as tight frame and no DC leakage. Furthermore, their approximation orders can be determined from the desired approximation accuracy. The effectiveness of our approach is evaluated by comparing them with existing spectral graph wavelets and Filter Banks.
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UNEQUAL LENGTH FIRST-ORDER LINEAR-PHASE Filter Banks FOR EFFICIENT IMAGE CODING
2015Co-Authors: Yuichi Tanaka, Masaaki Ikehara, Truong Q. NguyenAbstract:In this paper, we present the structure and design method for a first-order linear-phase Filter bank (FOLPFB) which has unequal Filter lengths in its synthesis bank (UFLPFB). A FOLPFB is a general-ized version of biorthogonal LPFBs regarding their synthesis Filter lengths. Ringing artifact is the main disadvantage of image coding based on FOLPFBs. UFLPFBs can reduce the ringing artifacts as well as approximate smooth regions well. Index Terms — First-order linear-phase Filter Banks, biorthogo-nal Filter Banks, unequal length Filter Banks, image coding. 1
Martin Vetterli - One of the best experts on this subject based on the ideXlab platform.
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pyramidal directional Filter Banks and curvelets
International Conference on Image Processing, 2001Co-Authors: Martin VetterliAbstract:A flexible multiscale and directional representation for images is proposed. The scheme combines directional Filter Banks with the Laplacian pyramid to provide a sparse representation for two-dimensional piecewise smooth signals resembling images. The underlying expansion is a frame and can be designed to be a tight frame. Pyramidal directional Filter Banks provide an effective method to implement the digital curvelet transform. The regularity issue of the iterated Filters in the directional Filter bank is examined.
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oversampled Filter Banks
IEEE Transactions on Signal Processing, 1998Co-Authors: Zoran Cvetkovic, Martin VetterliAbstract:Perfect reconstruction oversampled Filter Banks are equivalent to a particular class of frames in l/sup 2/(Z). These frames are the subject of this paper. First, the necessary and sufficient conditions of a Filter bank for implementing a frame or a tight frame expansion are established, as well as a necessary and sufficient condition for perfect reconstruction using FIR Filters after an FIR analysis. Complete parameterizations of oversampled Filter Banks satisfying these conditions are given. Further, we study the condition under which the frame dual to the frame associated with an FIR Filter bank is also FIR and give a parameterization of a class of Filter Banks satisfying this property. Then, we focus on non-subsampled Filter Banks. Non-subsampled Filter Banks implement transforms similar to continuous-time transforms and allow for very flexible design. We investigate the relations of these Filter Banks to continuous-time Filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two-channel Filter Banks that yield highly regular wavelets with a given number of vanishing moments.
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orthogonal time varying Filter Banks and wavelet packets
IEEE Transactions on Signal Processing, 1994Co-Authors: Cormac Herley, Martin VetterliAbstract:Considers the construction of orthogonal time-varying Filter Banks. By examining the time domain description of the two-channel orthogonal Filter bank the authors find it possible to construct a set of orthogonal boundary Filters, which allows to apply the Filter bank to one-sided or finite-length signals, without redundancy or distortion. The method is constructive and complete. There is a whole space of orthogonal boundary solutions, and there is considerable freedom for optimization. This may be used to generate subband tree structures where the tree varies over time, and to change between different Filter sets. The authors also show that the iteration of discrete-time time-varying Filter Banks gives continuous-time bases, just as in the stationary case. This gives rise to wavelet, or wavelet packet, bases for half-line and interval regions. >
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perfect reconstruction Filter Banks with rational sampling factors
IEEE Transactions on Signal Processing, 1993Co-Authors: Jelena Kovačević, Martin VetterliAbstract:An open problem, namely, how to construct perfect reconstruction Filter Banks with rational sampling factors, is solved. Such Filter Banks have N branches, each one having a sampling factor of p i/qi, and their sum equals one. In this way, the well-known theory of Filter Banks with uniform band splitting is extended to allow for nonuniform divisions of the spectrum. This can be very useful in the analysis of speech and music. The theory relies on two transforms. The first transform leads to uniform Filter Banks having polyphase components as individual Filters. The other results in a uniform Filter bank containing shifted versions of same Filters. This, in turn, introduces dependencies in design, and is left for future work. As an illustration, several design examples for the (2/3, 1/3) case are given. Filter Banks are then classified according to the possible ways in which they can be built. It is shown that some cases cannot be solved even with ideal Filters (with real coefficients)
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wavelets and Filter Banks theory and design
IEEE Transactions on Signal Processing, 1992Co-Authors: Martin Vetterli, Cormac HerleyAbstract:The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, Filter Banks, and multiresolution signal processing are explored. A brief review is given of perfect reconstruction Filter Banks, which can be used both for computing the discrete wavelet transform, and for deriving continuous wavelet bases, provided that the Filters meet a constraint known as regularity. Given a low-pass Filter, necessary and sufficient conditions for the existence of a complementary high-pass Filter that will permit perfect reconstruction are derived. The perfect reconstruction condition is posed as a Bezout identity, and it is shown how it is possible to find all higher-degree complementary Filters based on an analogy with the theory of Diophantine equations. An alternative approach based on the theory of continued fractions is also given. These results are used to design highly regular Filter Banks, which generate biorthogonal continuous wavelet bases with symmetries. >
T Q Nguyen - One of the best experts on this subject based on the ideXlab platform.
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a simplified lattice structure of first order linear phase Filter Banks
European Signal Processing Conference, 2007Co-Authors: Yuichi Tanaka, Masaaki Ikehara, T Q NguyenAbstract:A simplified lattice structure for first-order linear-phase Filter Banks (FOLPFBs) is presented in this paper. A FOLPFB is a generalized version of biorthogonal linear-phase Filter Banks regarding their synthesis Filter lengths. FOLPFBs' structure is more complicated and has more parameters than that in other FBs. We propose a method to reduce their redundant parameters without losing their properties. Moreover, regularity can be imposed which reduces the design freedom as well as improves the perceptual quality in image coding.
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a general formulation of modulated Filter Banks
IEEE Transactions on Signal Processing, 1999Co-Authors: P N Heller, Tanja Karp, T Q NguyenAbstract:This paper presents a general framework for maximally decimated modulated Filter Banks. The theory covers the known classes of cosine modulation and relates them to complex-modulated Filter Banks. The prototype Filters have arbitrary lengths, and the overall delay of the Filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation-modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype Filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization).
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performance analysis of multicarrier modulation systems using cosine modulated Filter Banks
International Conference on Acoustics Speech and Signal Processing, 1999Co-Authors: S Govardhanagiri, Tanja Karp, P N Heller, T Q NguyenAbstract:We compare the performance of biorthogonal cosine modulated transmultiplexer Filter Banks with today's multicarrier modulation systems whose transceivers are based on DFT. In contrast to early works on transmultiplexer Filter Banks that concentrated on the derivation of perfect reconstruction constraints of the Filter bank or prototype design, this study takes into consideration a typical twisted pair copper line transmission channel into consideration and examines the influence of different system parameters as Filter length, number of channels, and the overall system delay on the distortion at the receiver. Biorthogonal Filter Banks have the advantage that Filter length and overall system delay can be chosen independently. Restricting the equalizer at the receiver to a single scalar tap per subchannel, we show that cosine-modulated Filter Banks outperform DFT based multicarrier systems without a guard interval and obtain a similar performance to DFT based systems with a guard interval and time domain equalization but at a lower computational cost and a higher throughput data rate.
Akie Sakiyama - One of the best experts on this subject based on the ideXlab platform.
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two channel critically sampled graph Filter Banks with spectral domain sampling
IEEE Transactions on Signal Processing, 2019Co-Authors: Akie Sakiyama, Yuichi Tanaka, Kana Watanabe, Antonio OrtegaAbstract:We propose two-channel critically-sampled Filter Banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable properties: first, perfect reconstruction regardless of the characteristics of the underlying graphs and graph variation operators; and second, a symmetric structure; i.e., both analysis and synthesis Filter Banks are built using similar building blocks. Along with the structure of the Filter Banks, this paper also proves the general criterion for perfect reconstruction and theoretically shows that the vertex and spectral domain sampling coincide for a special case. The effectiveness of our approach is evaluated by comparing its performance in nonlinear approximation and denoising with various conventional graph transforms.
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critically sampled graph Filter Banks with polynomial Filters from regular domain Filter Banks
Signal Processing, 2017Co-Authors: D B H Tay, Yuichi Tanaka, Akie SakiyamaAbstract:Graph signal processing deals with the processing of signals defined on irregular domains and is an emerging area of research. Graph Filter Banks allow the wavelet transform to be extended for processing graph signals. Sakiyama and Tanaka (2015) 22 recently proposed a technique to convert linear-phase biorthogonal Filter Banks for regular domain signals to biorthogonal graph Filter Banks. Perfect reconstruction is preserved using the technique but the resulting spectral Filter functions are transcendental and not polynomial. Polynomial function Filters are desired for the localization property and implementation efficiency. In this work we present alternative techniques to perform the conversion. Perfect reconstruction is preserved with the proposed techniques and the resulting spectral Filters are polynomial functions. HighlightsWe design Filter Banks for signal defined over bipartite graphs.Spectral Filters are polynomials resulting in localization and efficient implementation.Technique is based on converting 1D regular domain Filter Banks.Perfect reconstruction is exactly preserved and spectral response shape is almost preserved.
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construction of undersampled graph Filter Banks via row subset selection
IEEE Global Conference on Signal and Information Processing, 2016Co-Authors: Akie Sakiyama, Yuichi TanakaAbstract:This paper introduces a construction method of M-channel under-sampled spectral graph Filter Banks. They can be applied to any kind of undirected graphs, use arbitrary critically sampled or oversampled analysis Filters, and obtain low redundancy, which is less than 1, regardless of the number of the analysis Filters. We formulate the construction problem as a row subset selection method of the transform matrix of the prototype (critically sampled or oversampled) Filter Banks. In the experiment, a graph signal on Minnesota Traffic Graph is decomposed to examine the performance of our spectral graph Filter Banks.
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spectral graph wavelets and Filter Banks with low approximation error
IEEE Transactions on Signal and Information Processing over Networks, 2016Co-Authors: Akie Sakiyama, Kana Watanabe, Yuichi TanakaAbstract:We propose Filter Banks in the graph spectral domain, where each Filter is defined by a sum of sinusoidal waves. The main advantages of these Filter Banks are that (a) they have low approximation errors even if a lower-order shifted Chebyshev polynomial approximation is used, (b) the upper bound of the error after the $p$ th order Chebyshev polynomial approximation can be calculated rigorously without complex calculations, and (c) their parameters can be efficiently obtained from any real-valued linear phase finite impulse response Filter Banks in regular signal processing. The proposed Filter bank has the same Filter characteristics as the corresponding classical Filter bank in the frequency domain and inherits the original properties, such as tight frame and no DC leakage. Furthermore, their approximation orders can be determined from the desired approximation accuracy. The effectiveness of our approach is evaluated by comparing them with existing spectral graph wavelets and Filter Banks.
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m channel oversampled perfect reconstruction Filter Banks for graph signals
International Conference on Acoustics Speech and Signal Processing, 2014Co-Authors: Yuichi Tanaka, Akie SakiyamaAbstract:This paper proposes M-channel oversampled Filter Banks for graph signals. The Filter set satisfies the perfect reconstruction condition. A method of designing oversampled graph Filter Banks is presented which allows us to design Filters with arbitrary parameters, unlike the conventional critically-sampled graph Filter Banks. The practical performance of the proposed Filter Banks is validated through graph signal denoising experiments.
