Passband Delay Research Articles

MINIMUM PHASE SELECTIVE BANDPASS DIGITAL FILTERS WITH CONTROLLED PASS-BAND LOSS AND DELAY

A simple numerical procedure is described for the construction of minimum phase selective band-pass digital filters satisfying simultaneous pass-band amplitude and phase constraints for any specified stop-band loss. It is shown that, if the pass-band loss of the filter is expressed as a linear combination of cosine functions, then the filter's group delay can be linearly expressed in terms of these functions together with any stop-band loss constraints. The simplex method of linear programming can then be invoked to minimize the pass-band delay deviation from constancy for any specified peak pass-band loss. Tlie_resulting transfer functions are shown to be less sensitive with reference to coefficients trancations. Illustrative examples are also given.

Image-parameter approximations for designing linear-phase filters

The stopband loss of a filter with arbitrary loss poles and an equal-ripple passband can be approximated extremely accurately by the loss of a related image-parameter filter. When the actual loss is greater than about 1 Np, its difference \alpha_{d} from the image loss is almost completely independent of frequency and is a function only of the passband ripple size. This approximation has been widely used in filter design since it was described by Darlington in 1939. The passband delay can also be approximated by the delay of the same image-parameter filter, but the difference \tau_{d} between the two delays is, unfortunately, not a constant but a fairly complicated function of frequency. The paper shows that \tau_{d} is the minimum delay corresponding to \alpha_{d} and that an approximation to \tau_{d} can be derived by taking the Hilbert transform of a spline function which approximates \alpha_{d} over the whole stopband. The sum of the image delay and this approximation to \tau_{d} represents the actual delay very accurately; both functions and their partial derivatives with respect to the poles can be computed quickly and simply. The two approximations, to loss and delay, can be used as the basis of a fast iterative program for designing high-degree linear-phase filters meeting an arbitrary specification on the stopband loss.

Low sensitivity active filters with predetermined group delay and Chebyshev stopband attenuation†

This paper presents a now class of transfer functions of odd degree with a controllable passband delay distortion and equal-ripple stopband attenuation which arc characterized by a low value of dominant pole Q factor. These functions are obtained by combining the technique of increasing critical polo multiplicity with a special typo of equal ripple approximation to a constant group delay, referred to as the constrained Chebyshev delay approximation. The stopband magnitude performance is improved by adding real frequency transmission zeros which do not affect the phase but completely suppress the output at some frequencies. When compared with the unconstrained equal-ripple delay approximant of Abele, the polynomial in the denominator of the rational transfer function provides an extra degree of freedom which enables one either to increase the roll-off of the attenuation characteristic in the transition region, or to improve the time-domain performance of the resulting network. Tables are presented which in...

Transfer functions for pulse forming active networks with low dominant pole q factor

AbstractA new class of all pole transfer functions of odd degree having the dominant pole Q factor of order of unity is described. Higher order transfer functions are derived from the third order function of a special class of Chebyshev delay approximation by increasing the multiplicity of the pair of complex poles under the constraint that the passband delay distortion remains within any prescribed maximum value. The specified delay distortion, acting as a free parameter, entails a tradeoff between the frequency and time domain characteristics of the resulting filters thus enabling a large variety of specifications to be met in practical design. These functions are primarily intended for pulse application but they can also be used advantageously in those instances where the magnitude response is of prime importance.