The Experts below are selected from a list of 117 Experts worldwide ranked by ideXlab platform
P P Vaidyanathan - One of the best experts on this subject based on the ideXlab platform.
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extending classical multirate signal processing theory to graphs part ii m channel filter banks
IEEE Transactions on Signal Processing, 2017Co-Authors: Oguzhan Teke, P P VaidyanathanAbstract:This paper builds upon the basic theory of multirate systems for graph signals developed in the companion paper (Part I) and studies $M$ -channel polynomial filter banks on graphs. The behavior of such graph filter banks differs from that of classical filter banks in many ways, the precise details depending on the eigenstructure of the adjacency matrix $\boldsymbol {A}$ . It is shown that graph filter banks represent, (linear and) periodically, shift-variant systems only when $\boldsymbol {A}$ satisfies the noble identity conditions developed in Part I. It is then shown that perfect reconstruction graph filter banks can always be developed when $\boldsymbol {A}$ satisfies the eigenvector structure satisfied by $M$ -block cyclic graphs and has distinct eigenvalues (further restrictions on eigenvalues being unnecessary for this). If $\boldsymbol {A}$ is actually $M$ -block cyclic then these PR filter banks indeed become practical, i.e., arbitrary filter polynomial orders are possible, and there are robustness advantages. In this case, the PR condition is identical to PR in classical filter banks—any classical PR example can be converted to a graph PR filter bank on an $M$ -block cyclic graph. It is shown that for $M$ -block cyclic graphs with all eigenvalues on the unit circle, the frequency responses of filters have meaningful correspondence with classical filter banks. Polyphase representations are then developed for graph filter banks and utilized to develop alternate conditions for Alias Cancellation and perfect reconstruction, again for graphs with specific eigenstructures. It is then shown that the eigenvector condition on the graph can be relaxed by using similarity transforms.
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Extending Classical Multirate Signal Processing Theory to Graphs—Part II: M-Channel Filter Banks
IEEE Transactions on Signal Processing, 2017Co-Authors: Oguzhan Teke, P P VaidyanathanAbstract:This paper builds upon the basic theory of multirate systems for graph signals developed in the companion paper (Part I) and studies $M$ -channel polynomial filter banks on graphs. The behavior of such graph filter banks differs from that of classical filter banks in many ways, the precise details depending on the eigenstructure of the adjacency matrix $\boldsymbol {A}$ . It is shown that graph filter banks represent, (linear and) periodically, shift-variant systems only when $\boldsymbol {A}$ satisfies the noble identity conditions developed in Part I. It is then shown that perfect reconstruction graph filter banks can always be developed when $\boldsymbol {A}$ satisfies the eigenvector structure satisfied by $M$ -block cyclic graphs and has distinct eigenvalues (further restrictions on eigenvalues being unnecessary for this). If $\boldsymbol {A}$ is actually $M$ -block cyclic then these PR filter banks indeed become practical, i.e., arbitrary filter polynomial orders are possible, and there are robustness advantages. In this case, the PR condition is identical to PR in classical filter banks—any classical PR example can be converted to a graph PR filter bank on an $M$ -block cyclic graph. It is shown that for $M$ -block cyclic graphs with all eigenvalues on the unit circle, the frequency responses of filters have meaningful correspondence with classical filter banks. Polyphase representations are then developed for graph filter banks and utilized to develop alternate conditions for Alias Cancellation and perfect reconstruction, again for graphs with specific eigenstructures. It is then shown that the eigenvector condition on the graph can be relaxed by using similarity transforms.
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Theory and design of two-parallelogram filter banks
IEEE Transactions on Signal Processing, 1996Co-Authors: P. P. Vaidyanathan, P P VaidyanathanAbstract:It is well known that the analysis and synthesis filters of orthonormal DFT filter banks can not have good frequency selectivity. The reason for this is that each of the analysis and synthesis filters have only one passband. Such frequency stacking (or configuration) in general does not allow Alias Cancellation when the individual filters have good stopband attenuation. A frequency stacking of this nature is called nonpermissible and should be avoided if good filters are desired. In a usual M-channel filter bank with real-coefficient filters, the analysis and synthesis filters have two passbands. It can be shown that the configuration is permissible in this case. Many designs proposed in the past demonstrate that filter banks with such configurations can have perfect reconstruction and be good filters at the same time. We develop the two-parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of two parallelograms. The two-parallelogram filter banks are analyzed from a pictorial viewpoint by exploiting the concept of permissibility. Based on this analysis, we construct and design a special type of two-parallelogram filter banks, namely, cosine-modulated filter banks (CMFB). In two-parallelogram CMFB, the analysis and synthesis filters are cosine-modulated versions of a prototype that has a parallelogram support. Necessary and sufficient conditions for perfect reconstruction of two-parallelogram CMFB are derived.
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Results on Biorthogonal Filter Banks
Applied and Computational Harmonic Analysis, 1994Co-Authors: I. Djokovic, P P VaidyanathanAbstract:Abstract For a maximally decimated nonuniform filter bank, the perfect reconstruction (PR) property is equivalent to biorthogonality. We start from this result and derive a number of properties of PR filter banks. For example, no two integer decimators in a biorthogonal system can be coprime; moreover, if all analysis and synthesis filters have unit energy, then perfect reconstruction is equivalent to orthonormality. We also generalize the Nyquist and power complementary properties of orthonormal filter banks, for the biorthogonal case. We then show that whenever the decimation ratios are such that biorthogonality is possible with rational filters, it is, in particular, possible to obtain orthonormality with rational filters. This is done by developing an orthonormalization procedure. While reminiscent of the Gram–Schmidt approach, the procedure converges in a finite number of steps and furthermore preserves the filter-bank-like form of the basis functions. We also show how this technique can be applied for the decorrelation of subband signals. We will consider the problem of Alias Cancellation and obtain a generalization of a previously known necessary condition called compatibility.
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Results on Biorthonormal Filter Banks
1993Co-Authors: I. Djokovic, P P VaidyanathanAbstract:Abstract : For a maximally decimated nonuniform filter bank, the perfect reconstruction (PR) property is equivalent to biorthonormality. We start from this result and derive a number of properties of PR filter banks. For example, no two integer decimators in a biorthonormal system can be coprime; moreover if all analysis and synthesis filters have unit energy, then perfect reconstruction is equivalent to orthonormality. We also generalize the Nyquist and power complementary properties of orthonormal filter banks, for the biorthonormal case. We then show that whenever the decimation ratios are such that biorthonormality is possible with rational filters, it is in particular possible to obtain orthonormality with rational filters. This is done by developing an orthonormalization procedure. While reminiscent of the Gram-Schmidt approach, the procedure converges in a finite number of steps and furthermore preserves the filter-bank Eke form of the basis functions. We then modify the orthonormalization procedure for the application of subband decorrelation. It will be demonstrated that mere decorrelation of subband signals does not necessarily optimize the coding gain of a system. Finally we consider the problem of Alias Cancellation, and obtain a generalization of a previously known necessary condition called compatibility.
Truong Q. Nguyen - One of the best experts on this subject based on the ideXlab platform.
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Partial spectrum reconstruction using digital filter banks
IEEE Transactions on Signal Processing, 1993Co-Authors: Truong Q. NguyenAbstract:The problem of reconstructing a part of the spectrum is reduced to designing the filter bank to satisfy a set of conditions. For the case considered here, these conditions cannot be satisfied simultaneously, so perfect reconstruction is not possible. The necessary and sufficient conditions on the filters so that the resulting filter bank cancels most Alias components are found. Such filter banks are called partial Alias Cancellation filter banks. The product of the polyphase transfer matrices of these filter banks must be a block pseudocirculant matrix. An algorithm design procedure is discussed, and examples are given to demonstrate the theory. >
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ICASSP - On the problem of reconstructing a segment of a wideband signal using a digital filter bank
[Proceedings] ICASSP 91: 1991 International Conference on Acoustics Speech and Signal Processing, 1991Co-Authors: Truong Q. NguyenAbstract:The design process is reduced to designing the filter bank to satisfy a set of conditions and it is known that the reconstructed signal always possesses some Alias and distortion. It is the present objective to find the necessary and sufficient conditions on the filters so that the resulting QMF (quadrature mirror filter) bank cancels most Alias components. Having found these conditions, the author suggests an algorithm to design the PAC (partial Alias Cancellation) QMF bank. Examples are given to demonstrate the theory. >
Oguzhan Teke - One of the best experts on this subject based on the ideXlab platform.
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extending classical multirate signal processing theory to graphs part ii m channel filter banks
IEEE Transactions on Signal Processing, 2017Co-Authors: Oguzhan Teke, P P VaidyanathanAbstract:This paper builds upon the basic theory of multirate systems for graph signals developed in the companion paper (Part I) and studies $M$ -channel polynomial filter banks on graphs. The behavior of such graph filter banks differs from that of classical filter banks in many ways, the precise details depending on the eigenstructure of the adjacency matrix $\boldsymbol {A}$ . It is shown that graph filter banks represent, (linear and) periodically, shift-variant systems only when $\boldsymbol {A}$ satisfies the noble identity conditions developed in Part I. It is then shown that perfect reconstruction graph filter banks can always be developed when $\boldsymbol {A}$ satisfies the eigenvector structure satisfied by $M$ -block cyclic graphs and has distinct eigenvalues (further restrictions on eigenvalues being unnecessary for this). If $\boldsymbol {A}$ is actually $M$ -block cyclic then these PR filter banks indeed become practical, i.e., arbitrary filter polynomial orders are possible, and there are robustness advantages. In this case, the PR condition is identical to PR in classical filter banks—any classical PR example can be converted to a graph PR filter bank on an $M$ -block cyclic graph. It is shown that for $M$ -block cyclic graphs with all eigenvalues on the unit circle, the frequency responses of filters have meaningful correspondence with classical filter banks. Polyphase representations are then developed for graph filter banks and utilized to develop alternate conditions for Alias Cancellation and perfect reconstruction, again for graphs with specific eigenstructures. It is then shown that the eigenvector condition on the graph can be relaxed by using similarity transforms.
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Extending Classical Multirate Signal Processing Theory to Graphs—Part II: M-Channel Filter Banks
IEEE Transactions on Signal Processing, 2017Co-Authors: Oguzhan Teke, P P VaidyanathanAbstract:This paper builds upon the basic theory of multirate systems for graph signals developed in the companion paper (Part I) and studies $M$ -channel polynomial filter banks on graphs. The behavior of such graph filter banks differs from that of classical filter banks in many ways, the precise details depending on the eigenstructure of the adjacency matrix $\boldsymbol {A}$ . It is shown that graph filter banks represent, (linear and) periodically, shift-variant systems only when $\boldsymbol {A}$ satisfies the noble identity conditions developed in Part I. It is then shown that perfect reconstruction graph filter banks can always be developed when $\boldsymbol {A}$ satisfies the eigenvector structure satisfied by $M$ -block cyclic graphs and has distinct eigenvalues (further restrictions on eigenvalues being unnecessary for this). If $\boldsymbol {A}$ is actually $M$ -block cyclic then these PR filter banks indeed become practical, i.e., arbitrary filter polynomial orders are possible, and there are robustness advantages. In this case, the PR condition is identical to PR in classical filter banks—any classical PR example can be converted to a graph PR filter bank on an $M$ -block cyclic graph. It is shown that for $M$ -block cyclic graphs with all eigenvalues on the unit circle, the frequency responses of filters have meaningful correspondence with classical filter banks. Polyphase representations are then developed for graph filter banks and utilized to develop alternate conditions for Alias Cancellation and perfect reconstruction, again for graphs with specific eigenstructures. It is then shown that the eigenvector condition on the graph can be relaxed by using similarity transforms.
Jelena Kovacevic - One of the best experts on this subject based on the ideXlab platform.
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subband coding systems incorporating quantizer models
IEEE Transactions on Image Processing, 1995Co-Authors: Jelena KovacevicAbstract:A new method for dealing with the effects of quantization in a subband system is proposed. It uses the "gain plus additive noise" linear model for the Lloyd-Max quantizer. Based on this, it is demonstrated how, by an appropriate choice of synthesis filters, one can cancel all signal-dependent errors at the output of the system. The only remaining error is random in nature and not correlated with the input signal. We therefore have a tradeoff between the error being only random or having signal-dependent components as well (since the error variances in both cases are comparable). As a result of having only a random error, it is possible to reduce this error using, for example, a noise removal technique. The result is then extended to the case where the input is a multidimensional signal, and arbitrary sampling lattices are used, as well as to the QMF (Alias Cancellation) case. To demonstrate the validity of the proposed approach, two types of experiments on images are carried out: In a toy example, it is shown that using noise removal could be beneficial. For a more realistic coding scheme, however, it is demonstrated that even in the case when the model is no longer valid (when some of the subbands are discarded), the output error is still much less correlated with the input signal as opposed to the commonly used subband system, while visually, the reconstructed images look very similar. >
Philip N. Garner - One of the best experts on this subject based on the ideXlab platform.
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Filter Bank Design for Subband Adaptive Beamforming and Application to Speech Recognition
2008Co-Authors: Kenichi Kumatani A, Stefan Schacht B, John Mcdonough B, Dietrich Klakow B, Weifeng Li A, Kenichi Kumatani, John Mcdonough, Stefan Schacht, Dietrich Klakow, Philip N. GarnerAbstract:Abstract. e present a new filter bank design method for subband adaptive beamforming. Filter bank design for adaptive filtering poses many problems not encountered in more traditional applications such as subband coding of speech or music. The popular class of perfect reconstruction filter banks is not well-suited for applications involving adaptive filtering because perfect reconstruction is achieved through Alias Cancellation, which functions correctly only if the outputs of individual subbands are not subject to arbitrary magnitude scaling and phase shifts. In this work, we design analysis and synthesis prototypes for modulated filter banks so as to minimize each Aliasing term individually. We then show that the total response error can be driven to zero by constraining the analysis and synthesis prototypes to be Nyquist(M) filters. We show that the proposed filter banks are more robust for Aliasing caused by adaptive beamforming than conventional methods. Furthermore, we demonstrate the effectiveness of our design technique through a set of automatic speech recognition experiments on the multi-channel, farfield speech data from the PASCAL Speech Separation Challenge. In our system, speech signals are first transformed into the subband domain with the proposed filter banks, and thereafter the subband components are processed with a beamforming algorithm. Following beamforming
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Filter Bank Design for Subband Adaptive Beamforming and Application to Speech Recognition
2008Co-Authors: Kenichi Kumatani, John Mcdonough, Stefan Schacht, Dietrich Klakow, Philip N. GarnerAbstract:begin{abstract} We present a new filter bank design method for subband adaptive beamforming. Filter bank design for adaptive filtering poses many problems not encountered in more traditional applications such as subband coding of speech or music. The popular class of perfect reconstruction filter banks is not well-suited for applications involving adaptive filtering because perfect reconstruction is achieved through Alias Cancellation, which functions correctly only if the outputs of individual subbands are not subject to arbitrary magnitude scaling and phase shifts. In this work, we design analysis and synthesis prototypes for modulated filter banks so as to minimize each Aliasing term individually. We then show that the total response error can be driven to zero by constraining the analysis and synthesis prototypes to be Nyquist($M$) filters. We show that the proposed filter banks are more robust for Aliasing caused by adaptive beamforming than conventional methods. Furthermore, we demonstrate the effectiveness of our design technique through a set of automatic speech recognition experiments on the multi-channel, far-field speech data from the PASCAL Speech Separation Challenge. In our system, speech signals are first transformed into the subband domain with the proposed filter banks, and thereafter the subband components are processed with a beamforming algorithm. Following beamforming, post-filtering and binary masking are performed to further enhance the speech by removing residual noise and undesired speech. The experimental results prove that our beamforming system with the proposed filter banks achieves the best recognition performance, a 39.6% word error rate (WER), with half the amount of computation of that of the conventional filter banks while the perfect reconstruction filter banks provided a 44.4% WER.