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Variable digital filters (VDFs) are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied online. In this paper, we investigate the design of VDFs with discrete coefficients as a means of achieving low complexity and efficient hardware implementation. The filter coefficients are expressed as the sum of signed power-of-two terms with a restriction on the total number of power-of-two for the filter coefficients. An efficient design procedure is proposed that includes an improved method for handling the quantization of the VDF coefficients for both the min--max and the least-square criteria leading to an optimum quantized solution. For the least-square criterion, a reduced search region around the optimum quantized solution is further constructed and the branch and bound method in conjunction with an efficient branch cutting scheme is presented to search for an optimum solution in this reduced region. Index Terms--Finite-impulse response (FIR) variable digital filter (VDF), least-square criteria, min--max, optimization, signed power-of-two (SPT) coefficients.

Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied online. In this brief, we present a formulation that allows the tradeoff between the total squared error and the maximum deviation from the desired response in the passband and stopband. With this formulation, the maximum deviation can be reduced below the least-square solution with only a slight change in the performance of the total squared error. Similarly, the total squared error can be reduced below the minmax solution with a minor change in the maximum deviation from the minmax solution. Index Terms--Least-square criterion, min-max criterion, peak gain constraint, variable digital filter (VDF).

An innovative approach is proposed for the design of minimum-phase digital filters as the sum of two allpass functions. It relies on the cepstrum technique.

Research into the construction of linear-phase digital filters is presented. A new computational method which offers a solution to the semi-infinite quadratic optimization question is proposed.

This paper considers the designs of the periodic window functions in the filter window banks. First, the filter window bank with the constant synthesis periodic window functions is considered. The total number of the nonzero coefficients in the impulse responses of the analysis periodic window functions is minimized subject to the near perfect reconstruction condition. This is an norm optimization problem. To find its solution, the norm optimization problem is approximated by the norm optimization problem. Then, the column of the constraint matrix corresponding to the element in the solution with the smallest magnitude is removed. Next, it is tested whether the feasible set corresponding to the new norm optimization problem is empty or not. By repeating the above procedures, a solution of the norm optimization problem is obtained. Second, the filter window bank with the time varying synthesis periodic window functions is considered. Likewise, the design of the periodic window functions in both the analysis periodic window functions and the synthesis periodic window functions is formulated as an optimization problem. However, this norm optimization problem is subject to a quadratic matrix inequality constraint. To find its solution, the set of the synthesis periodic window functions is initialized. Then, the set of the analysis periodic window functions is optimized based on the initialized set of the synthesis periodic window functions. Next, the set of the synthesis periodic window functions is optimized based on the found set of the analysis periodic window functions. Finally, these two procedures are iterated. It is shown that the iterative algorithm converges. A design example of a filter window bank with the constant synthesis periodic window functions and a design example of a filter window bank with the time varying synthesis periodic window functions are illustrated. It is shown that the near perfect reconstruction condition is satisfied, whereas this is not the cases for the nonuniform filter banks with the conventional samplers and the conventional block samplers. [ABSTRACT FROM AUTHOR]

In this paper, we investigate robust design methods for broadband beamformers in reverberant environments. In the design formulation room reverberation as well as robustness to amplitude and phase mismatches in the microphones have been included. Particularly, the direct path and the reflections are separated in the design such that there is a penalty on the reflective part. This approach is different from the commonly studied problem of dereverberation of a single point source as the investigated design is made over a region in space. A single point derverberation is not a very practical approach due to a high sensitivity to position changes. Thus in order to obtain more practical microphone array designs, we study methods that optimize performance over areas in space. The design problem has been formulated in four different ways; (i) using direct path only representing a traditional beamformer design method, (ii) using a robust design method which considers robustness against the microphone characteristics (gain and phase) by optimizing the mean performance, (iii) by including room impulse response in the design and finally, (iv) using both robustness and room impulse response in the design. Simulation results show that robust direct path based beamformer can achieve approximately the same performance as including room response in the design in many reverberation environments. The proposed method provides robustness over larger variations in the reverberation environment. This means that the robust direct path based method which is based on mean variations in gain and phase can be used in low- to medium ( T 60 = 100–300 ms) reverberant environments with good result. [ABSTRACT FROM AUTHOR]

This paper investigates the design of non-uniform cosine modulated filter bank (CMFB) with both finite precision coefficients and infinite precision coefficients. The finite precision filter bank has been designed to reduce the computational complexity related to the multiplication operations in the filter bank. Here, non-uniform filter bank (NUFB) is obtained by merging the appropriate filters of an uniform filter bank. An efficient optimization approach is developed for the design of non-uniform CMFB with infinite precision coefficients. A new procedure based on the discrete filled function is then developed to design the filter bank prototype filter with finite precision coefficients. Design examples demonstrate that the designed filter banks with both infinite precision coefficients and finite precision coefficients have low distortion and better performance when compared with other existing methods. [ABSTRACT FROM AUTHOR]

The design of digital Laguerre networks with a complex desired frequency response and the Chebyshev error criterion is investigated. This nonlinear optimization problem in the complex domain can be converted to an equivalent semi-infinite linear programming problem. Additional constraints are introduced to control the group delay error (i.e., allowing approximate rather than exact linear phase). The Laguerre network with approximately linear phase in the passband can achieve the same desired specification as the conventional FIR filters with a smaller number of coefficients, especially for narrow-band specifications. Index Terms--Chebyshev error, digital Laguerre networks.