Low Delay Filter Banks with Perfect Reconstruction

The design of modulated filter banks with a low system delay and with perfect reconstruction will be shown. The filter lengths K can be chosen arbitrarily. The well known orthogonal filter banks have a system delay of K - 1 samples. The proposed filter banks can reduce this delay to N - 1 samples, where N is the number of bands. The design method uses a decomposition or factorization of the polyphase matrix into cascades of simple matrices. Several factorizations with different properties will be shown. A factorization will be introduced which is more general and needs fewer multiplications than previous approaches (K/2 + N). The resulting filter banks can have analysis and synthesis frequency responses that can be made different from each other, leading to biorthogonal filter banks. An optimization algorithm for the frequency response of the resulting filter banks will be given. Examples show the feasibility of designing even big filter banks with many bands with low system delay and high stopband attenuation

A Generalized Window Approach for Designing Transmultiplexers

This paper proposes a computational, very efficient, approach for designing a novel family of M-channel maximally decimated nearly perfect-reconstruction cosine-modulated transmultiplexers. This approach is referred to as the generalized windowing method for transmultiplexers because after knowing the transmission channel a proper weighted sum of the inter-channel and inter-symbol interferences can be properly taken into account in the optimization of the window function, unlike in other existing windowing techniques. The proposed approach has also the following two advantages. First, independent of the number of subchannels and the common order of the subchannel filters, the number of unknowns is only four. Second, the overall optimization procedure is made considerably fast by estimating the above-mentioned sum in terms of two novel measures, namely, the signal to inter-symbol and the signal to inter-channel interferences, which are very easy to evaluate. Furthermore, when the transmission channel is not considered in the design, a table is provided, which contains the parameters for designing the prototype filter directly by using the windowing method without any time-consuming optimization. When comparing the resulting transmultiplexers with the corresponding perfect-reconstruction designs (the same number of subchannels and same prototype filter order), the levels of interferences are practically the same. However, when the system is affected by a strong narrowband interference, the proposed transmultiplexers outperform their PR counterparts. Design examples are included illustrating the efficiency of the proposed design approach over other existing techniques based on the use of the windowing method

Residual echo signal in critically sampled subband acoustic echo cancellers based on IIR and FIR filter banks

Published versio

Filterbank optimization with convex objectives and the optimality of principal component forms

This paper proposes a general framework for the optimization of orthonormal filterbanks (FBs) for given input statistics. This includes as special cases, many previous results on FB optimization for compression. It also solves problems that have not been considered thus far. FB optimization for coding gain maximization (for compression applications) has been well studied before. The optimum FB has been known to satisfy the principal component property, i.e., it minimizes the mean-square error caused by reconstruction after dropping the P weakest (lowest variance) subbands for any P. We point out a much stronger connection between this property and the optimality of the FB. The main result is that a principal component FB (PCFB) is optimum whenever the minimization objective is a concave function of the subband variances produced by the FB. This result has its grounding in majorization and convex function theory and, in particular, explains the optimality of PCFBs for compression. We use the result to show various other optimality properties of PCFBs, especially for noise-suppression applications. Suppose the FB input is a signal corrupted by additive white noise, the desired output is the pure signal, and the subbands of the FB are processed to minimize the output noise. If each subband processor is a zeroth-order Wiener filter for its input, we can show that the expected mean square value of the output noise is a concave function of the subband signal variances. Hence, a PCFB is optimum in the sense of minimizing this mean square error. The above-mentioned concavity of the error and, hence, PCFB optimality, continues to hold even with certain other subband processors such as subband hard thresholds and constant multipliers, although these are not of serious practical interest. We prove that certain extensions of this PCFB optimality result to cases where the input noise is colored, and the FB optimization is over a larger class that includes biorthogonal FBs. We also show that PCFBs do not exist for the classes of DFT and cosine-modulated FBs

Design of multi-plet perfect reconstruction filter banks using frequency-response masking technique

This paper proposes a new design method for a class of two-channel perfect reconstruction (PR) filter banks (FBs) called multi-plet FBs with very sharp cutoff using frequency- response masking (FRM) technique. The multi-plet FBs are PR FBs and their frequency characteristics are controlled by a single subfilter. By recognizing the close relationship between the subfilter and the FRM-based halfband filter, very sharp cutoff PR multi-plet FBs can be realized with reduced implementation complexity. The design procedure is very general and it can be applied to both linear-phase and low-delay PR FBs. Design examples are given to demonstrate the usefulness of the proposed method. © 2008 IEEE.published_or_final_versio

On the design and multiplierless realization of perfect reconstruction triplet-based FIR filter banks and wavelet bases

This paper proposes new methods for the efficient design and realization of perfect reconstruction (PR) two-channel finite-impulse response (FIR) triplet filter banks (FBs) and wavelet bases. It extends the linear-phase FIR triplet FBs of Ansari et al. to include FIR triplet FBs with lower system delay and a prescribed order of K regularity. The design problem using either the minimax error or least-squares criteria is formulated as a semidefinite programming problem, which is a very flexible framework to incorporate linear and convex quadratic constraints. The K regularity conditions are also expressed as a set of linear equality constraints in the variables to be optimized and they are structurally imposed into the design problem by eliminating the redundant variables. The design method is applicable to linear-phase as well as low-delay triplet FBs. Design examples are given to demonstrate the effectiveness of the proposed method. Furthermore, it was found that the analysis and synthesis filters of the triplet FB have a more symmetric frequency responses. This property is exploited to construct a class of PR M-channel uniform FBs and wavelets with M = 2 L, where L is a positive integer, using a particular tree structure. The filter lengths of the two-channel FBs down the tree are approximately reduced by a factor of two at each level or stage, while the transition bandwidths are successively increased by the same factor. Because of the downsampling operations, the frequency responses of the final analysis filters closely resemble those in a uniform FB with identical transition bandwidth. This triplet-based uniform M-channel FB has very low design complexity and the PR condition and K regularity conditions are structurally imposed. Furthermore, it has considerably lower arithmetic complexity and system delay than conventional tree structure using identical FB at all levels. The multiplierless realization of these FBs using sum-of-power-of-two (SOPOT) coefficients and multiplier block is also studied. © 2004 IEEE.published_or_final_versio

Parity-check matrix calculation for paraunitary oversampled DFT filter banks

International audienceOversampled filter banks, interpreted as error correction codes, were recently introduced in the literature. We here present an efficient calculation and implementation of the parity-check polynomial matrices for oversampled DFT filter banks. If desired, the calculation of the partity-check polynomials can be performed as part of the prototype filter design procedure. We compare our method to those previously presented in the literature

New method for designing two-channel causal stable IIR perfect reconstruction filter banks and wavelet bases

A new method for designing two-channel causal stable IIR PR filter banks and wavelet bases is proposed. It is based on the structure previously proposed by Phoong et al. (1995). Such a filter bank is parameterized by two functions α(z) and β(z), which can be chosen as an all-pass function to obtain IIR filterbanks with very high stopband attenuation. One of the problems with this choice is that a bump of about 4 dB always exists near the transition band of the analysis and synthesis filters. The stopband attenuation of the high-pass analysis filter is also 10 dB lower than that of the low-pass filter. By choosing β(z) and α(z) as an all-pass function and a type-II linear-phase finite impulse response (FIR) function, respectively, the bumping can be significantly suppressed. In addition, the stopband attenuation of the high-pass filter can be controlled easily. The design problem is formulated as a polynomial approximation problem and is solved efficiently by the Remez exchange algorithm. The extension of this method to the design of a class of IIR wavelet bases is also considered.published_or_final_versio