Selective digital filters with quadratic phase

Abstract

Summary A method for design of a new class of digital infinite impulse response filters realized as parallel connection of two all‐pass filters is presented in this paper. A new approach to approximation of quadratic phase of all‐pass filter at all frequencies is given. Chosen parallel structure offers opportunity for realization of filters with arbitrary shape phase. The presented algorithm is based on all‐pass filter phase approximation. Phases of both all‐pass filters approximate ideal quadratic phase in minimax sense at all frequencies. Such filters can be applied for chirp signal compression or expansion. Magnitude characteristic of described filters is very selective and elliptic‐like. Obtained filters are compared with elliptic filter and group delay corrector in cascade. For the same specifications, much better results are achieved by the proposed filters. Parallel connection of all‐pass filters introduces lower signal delay, and for a given maximal phase, approximation error demands less complex network. Examples to illustrate the proposed method are given. Copyright © 2016 John Wiley & Sons, Ltd.

A New Method for Design of Selective Digital Iir Filters With Arbitrary Phase

“…In the previous work [12] the algorithm for design of selective filters with a quadratic phase is presented. This algorithm is based on approximation of an ideal quadratic phase 2 21…”

“…The novelty in this approach is that the same algorithm, presented in details in [12], can be used for design of a filter with linear phase. To achieve that, in ideal quadratic phase equation, the parameter a will be set to zero.…”

“…1). The parallel all-pass structure exhibits small sensitivity in all pass-bands [10][11][12], that makes them very suitable for practical implementation. At the same time, it is important to note that a real benefit will be achieved in the case when both of two complementary filters are of interest because only one additional adder is enough to realize the second filter.…”

“…In the case of a quadratic phase approximation [12], group delay of such filters is either linearly decreasing or linearly increasing, which makes them suitable for achieving a chirp signal compression or expansion. Thanks to this property, they can be implemented in radar and satellite systems, as well as in a wide range of telecommunication systems.…”

A Complexity Analysis of IIR Filters with an Approximately Linear Phase

“…The EC filters do not only fulfill the same magnitude specifications as the PA filters, but also provide a similar group delay error. According to (4), the PA filter can provide an arbitrary phase shape [19] if the delay line is substituted with an IIR all-pass filter of the same order. In that case both all-pass filter phases approximate the same predefined ideal phase of the chosen shape.…”