Abstract
In this contribution we present a method to design prototype filters of oversampling uniform complex-modulated FIR filter bank pairs. Especially, we present a noniterative two-step procedure: (i) design of analysis prototype filter with minimum group delay and approximately linear-phase frequency response in the passband and the transition band and (ii) Design of synthesis prototype filter such that the filter bank pairs distortion function approximates a linear-phase allpass function. Both aliasing and imaging are controlled by introducing sophisticated stopband constraints in both steps. Moreover, we investigate the delay properties of oversampling uniform complex-modulated FIR filter bank pairs in order to achieve the lowest possible filter bank delay. An illustrative design example demonstrates the potential of the design approach.
Highlights
A digital filter bank pair (FBP) is represented by a cascade connection of an analysis filter bank (AFB) for signal decomposition and a synthesis filter bank (SFB) for signal reconstruction
The former property is most important if the FBP is part of mobile equipment with tight energy constraints, most pronounced in hearing aids (HAs) [1], while the latter requirement must, for instance, be considered in two-way communication systems or HA, where the total group delay of the FBP shall not exceed 5–8 milliseconds [2, 3] to allow for sufficient margin for extensive subband signal processing
(1) In Section 2 being related to the first objective of this paper, we begin with a system-theoretic description and analysis of oversampling I-channel complex-modulated FIR filter bank pairs without subband signal manipulation, which supplements and extends the results reported in [16]
Summary
A digital filter bank pair (FBP) is represented by a cascade connection of an analysis filter bank (AFB) for signal decomposition and a synthesis filter bank (SFB) for signal reconstruction. As the objective function to be minimised we adopt a particular representation of the group delay [20], while the stopband magnitude specifications of the prototype filter, as derived in [7], serve as constraints to control subband signal aliasing or imaging, respectively. The AFB (or SFB) FIR prototype filter is designed subject to the stopband magnitude constraints, as given by [7], while the SFB (or AFB) prototype filter is fixed to the design obtained in the previous step By this procedure the AFB and SFB prototype filters’ magnitude responses are matched in the passbands and the transition bands without further consideration of the overall FBP group delay, aiming at minimum, possibly differing AFB and SFB prototype filter orders.
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