Allpass Phase Equalizers Research Articles

Design of 2-D FIR digital filters with specified magnitude and group delay responses by GA approach

An effective genetic algorithm (GA) approach is proposed for designing two-dimensional (2-D) real finite-duration impulse response (FIR) digital filters with complex-valued frequency responses. The method is extended from the one-dimensional (1-D) filter designs. By minimizing a quadratic measure of the error in the frequency band, the real-valued chromosomes of a population are evolved to get the filter coefficients. It is used to design two major classes of 2-D FIR digital filters including multi-band filters and all-pass phase equalizers. Two examples are presented to demonstrate the efficiency and effectiveness of this proposed approach.

Complex eigenfilter design of arbitrary complex coefficient FIR digital filters

The real eigenfilter approach is extended to complex cases for designing arbitrary complex finite impulse response (FIR) filters. By minimizing a quadratic measure of the error in the passband and stopband, a complex eigenvector of an appropriate complex, Hermitian symmetric, and positive-definite matrix is computed to get the filter coefficients. Several arbitrary magnitude and phase FIR filters, such as multiple passband complex filters and staircase-delay allpass phase equalizers, can be easily designed by this approach. This method can be easily extended to design 2-D complex FIR filters. If an appropriate iterative process is used, equiripple filters in the complex Chebyshev sense can be obtained. Several numerical design examples demonstrate the usefulness of the approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Eigen-approach for designing FIR filters and all-pass phase equalizers with prescribed magnitude and phase response

An effective eigenfilter approach is proposed for designing FIR filters with complex-valued frequency responses. By minimizing a quadratic measure of the error in the frequency band, an eigenvector of an appropriate matrix is computed to get the filter coefficients. The algorithm is easy and optimal in the least squares sense; it is used to design to major classes of FIR filters, including multiband filters, differentiators, Hilbert transformers, and all-pass phase. Several examples and comparisons to the existing linear programming methods are presented to demonstrate the flexibility and effectiveness of this approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design of real FIR filters with arbitrary complex frequency responses by two real Chebyshev approximations

Abstract Since the real coefficients of a FIR filter with arbitrary complex-valued desired frequency responses are neither symmetric nor antisymmetric, the Remez exchange algorithm cannot be applied directly. The problem can be solved by dividing the original complex approximation into two real ones such that the Remez exchange algorithm can be applied by slightly modifying the Parks-McClellan program. This method is much easier than the currently existing methods using linear programming or complex Chebyshev approximation, and the performance is satisfactory. More importantly, the magnitudes of the resultant complex errors are also equiripple as the direct complex Chebyshev approximation designs. Several numerical examples including a low-pass filter, a full-band differentiator, a wide-band Hilbert transformer, and a chirp-delay and sine-delay FIR all-pass phase equalizer are given to show the effectiveness of this approach.

Transfer functions for sharp cut-off filters with an equalized phase response

A method is presented for determining transfer functions of sharp cut-off low-pass and band-pass filters having small pass-band magnitude and group delay distortion. It is similar to the conventional approach in the sense that the minimum phase shift filter section and the all-pass phase equalizer section are designed separately and then connected in cascade. Unlike the latter, however, the present technique does not use the smallest possible order of function to realize the minimum phase-shift part of the network, but some redundant elements are permitted in order to simplify the design of phase-equalizer section. To this end, the prescribed magnitude rosponse is approximated by use of a recently introduced class of monotonic pass-band filters, referred to as LSM filters. It is shown that this leads to a reduction in the overall complexity of the network when compared with conventional Cauer filter and phase-equalizer combination. Also, the relative sensitivity of the resulting network taken with respect...