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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.

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.

We characterize the delay properties of uniformly modulated finite impulse response (FIR) filterbanks. Conditions on the permissable delay are developed for this class of filterbanks when the perfect reconstruction condition is relaxed. Accurate linear approximations for the phase and the group delay of the total filterbank are derived. These approximations allow linear phase or group delay constraints to be introduced in the filter optimization problem. A tractable quadratic optimization problem for the design of optimal analysis and synthesis filter prototypes is proposed. The problem involves the minimization of the aliasing distortion while constraining group delay and amplitude distortion. Thus, a new algorithm is presented to solve this optimization problem for the analysis and synthesis filterbanks simultaneously. Numerical examples are presented that confirm the theoretical results and verify that the approximations used are highly accurate. [ABSTRACT FROM AUTHOR]

We propose a numerically efficient technique to approximate the joint detection probability of a coherent multiple input multiple output (MIMO) receiver in the presence of inter-symbol interference (ISI) and additive white Gaussian noise (AWGN). This technique approximates the probability of detection by numerically integrating the product of the characteristic function (CF) of the received filtered signal with the Fourier transform of the multi-dimension decision region. Naturally, the accuracy of the approximation is dependent on the number of points in the numerical integration. The proposed method selects the number of points to integrate over by deriving bounds on the approximation error. As such, a reduction of up to 1/100^th of the number points can be achieved when comparing with existing single input single output (SISO) techniques. Simulation results demonstrate that the proposed method is highly accurate with the calculated errors being well within the bounded approximation error. In addition, the results are closely matched with those obtained using the Monte Carlo simulations with a typical error less than 10^-4 while requiring only a fraction of the computation time. [ABSTRACT FROM PUBLISHER]