Design of two-channel PR FIR filter banks with low system delay

IEEE International Symposium on Circuits and Systems, Geneva, Switzerland, 28-31 May 2000In this paper, a new approach for designing two-channel PR FIR filter banks with low system delay is proposed. It is based on the generalization of the structure previously proposed by Phoong et al. Such structurally PR filter banks are parameterized by two functions α(z) and β(z) which can be chosen as linear-phase FIR or allpass functions to construct FIR/IIR filter banks with good frequency characteristics. In this paper, the more general case of using different nonlinear-phase FIR functions for β(z) and α(z) is studied. As the linear-phase requirement is relaxed, higher stopband attenuation can still be achieved at low system delay. The design of the proposed low-delay filter banks is formulated as a complex polynomial approximation problem, which can be solved by the Remez exchange algorithm or analytic formula with very low complexity. The usefulness of the proposed algorithm is demonstrated by several design examples.published_or_final_versio

Theory and design of a class of M-channel IIR cosine-modulated filter banks

This letter proposes a method for designing a class of M-channel, causal, stable, perfect reconstruction (PR) IIR cosine-modulated filter banks (CMFB). The proposed CMFB has the same denominator for all its polyphase components in the prototype filter. Therefore, the PR condition is considerably simplified, and it is relatively simple to satisfy the PR and the casual-stable requirements of the IIR CMFB. Design examples show that the proposed IIR CMFB has sharper cutoff, higher stopband attenuation, and passband flatness than its FIR counterparts, especially when the system delay is small.published_or_final_versio

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

Theory and design of causal stable IIR PR cosine-modulated filter banks

This paper proposes a novel method for designing two-channel and M-channel causal stable IIR PR filter banks using cosine modulation. In particular, we show that the PR condition of the two-channel IIR filter banks is very similar to the two-channel FIR case. Using this formulation, it is relatively simple to satisfy the PR condition and to ensure that the filters are causal stable. Using a similar approach, we propose a new class of M-channel causal stable IIR cosine modulated filter banks. Design examples are given to demonstrate the usefulness of proposed approach.published_or_final_versio

New design method for two-channel perfect reconstruction IIR filter banks

In this paper, a new method for designing perfect reconstruction (PR) two-channel causal stable IIR filter banks is introduced. It is based on a structure previously proposed by Phoong et al. [2]. By using a combination of allpass and linear-phase FIR functions, the bumping problem found in the conventional structural PR filter bank is significantly suppressed. The design problem is formulated as a polynomial approximation problem and is solved effectively using the Remez exchange algorithm. Filter banks with flexible stopband attenuation and system delay can readily be obtained using the proposed algorithm.published_or_final_versio

Efficient method for designing two-channel PR FIR filter banks with low system delay

In this paper, an efficient method for designing perfect reconstruction (PR) two-channel finite impulse response (FIR) filter banks with low system delay is proposed. It is based on the use of nonlinear-phase FIR function in a structure previously proposed by Phoong et al. The design problem is formulated as a complex polynomial approximation problem and is solved effectively using the Remez exchange algorithm with very low design complexity. Design examples show that filter banks with flexible stopband attenuation and system delay can be readily obtained by the proposed algorithm.published_or_final_versio

Designing two-channel causal stable IIR PR filter banks and wavelet bases by model order reduction and constrained optimization

In this paper, two methods for designing two-channel causal stable IIR PR filter banks are introduced. The first method makes use of model reduction and constrained optimization to obtain a causal stable IIR filter bank from the structural PR FIR filter bank proposed in [2]. It yields better frequency characteristics than the original FIR filter bank and avoids the dump at π/2 when allpass filters are used. Using the 1-D to 2-D transformation proposed in [2], two dimensional PR IIR filter bank can readily be obtained from these prototypes. The second method is based on constrained optimization technique using the general PR condition. Using this technique, filter banks with low system delay and flexible frequency characteristics can be designed. The technique can also be modified to design causal stable IIR dyadic wavelet bases with added regularity conditions. A number of design examples are used to demonstrate the usefulness of the proposed design methods.published_or_final_versio

Design and multiplierless implementation of two-channel biorthogonal IIR filter banks with low system delay

An efficient method for the design of low-delay two-channel, perfect reconstruction IIR filter banks is proposed. The design problem is formulated in terms of minimax designs of a general stable IIR filter that can be obtained using semidefinite programming and an FIR filter that can be obtained using the Remez exchange algorithm. A multiplierless implementation on this filter bank is also proposed and investigated.published_or_final_versio

The factorization of M-channel FIR and IIR cosine-modulated filter banks and their multiplier-less realizations using sopot coefficients

The 47th Midwest Symposium on Circuits and Systems Conference Proceedings, Salt Lake City, Utah, USA, 25-28 July 2004This paper proposes a new factorization for the M-channel perfect reconstruction (PR) IIR Cosine-Modulated filter banks (CMFB) proposed previously by the authors. This factorization, which is based on the lifting scheme, is also complete for the PR FIR CMFB as well as the general two-channel PR IIR filter banks if the determinant of the polyphase matrix is equal to constant multiplies of signal delays. It can be used to convert a numerically optimized nearly PR CMFB to a structurally PR system. Furthermore, the arithmetic complexity of the FB using this structure can be reduced asymptotically by a factor of two. When the forward and inverse transforms are implemented with the same set of SOPOT coefficients, a multiplier-less CMFB can be obtained. Its arithmetic complexity is further reduced and it becomes very attractive for VLSI implementation.published_or_final_versio

Design and multiplier-less implementation of a class of two-channel PR FIR filterbanks and wavelets with low system delay

In this paper, a new method for designing two-channel PR FIR filterbanks with low system delay is proposed. It is based on the generalization of the structure previously proposed by Phoong et al. Such structurally PR filterbanks are parameterized by two functions (β(z) and α(z)) that can be chosen as linear-phase FIR or allpass functions to construct FIR/IIR filterbanks with good frequency characteristics. The case of using identical β(z) and α(z) was considered by Phoong et al. with the delay parameter M chosen as 2N - 1. In this paper, the more general case of using different nonlinear-phase FIR functions for β(z) and α(z) is studied. As the linear-phase constraint is relaxed, the lengths of β(z) and α(z) are no longer restricted by the delay parameters of the filterbanks. Hence, higher stopband attenuation can still be achieved at low system delay. The design of the proposed low-delay filterbanks is formulated as a complex polynomial approximation problem, which can be solved by the Remez exchange algorithm or analytic formula with very low complexity. In addition, the orders and delay parameters can be estimated from the given filter specifications using a simple empirical formula. Therefore, low-delay two-channel PR filterbanks with flexible stopband attenuation and cutoff frequencies can be designed using existing filter design algorithms. The generalization of the present approach to the design of a class of wavelet bases associated with these low-delay filterbanks and its multiplier-less implementation using the sum of powers-of-two coefficients are also studied.published_or_final_versio