All-Pass Filter Design Using Blaschke Interpolation

Obtaining a rational all-pass filter that matches a target phase response is a common problem in signal processing. Typical approaches have generally focused on optimizing filter coefficients while minimizing the deviation from the target phase response. However, these approaches typically do not of...

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Bibliographic Details
Published in:IEEE signal processing letters 2020, Vol.27, p.226-230
Main Authors: Appaiah, Kumar, Pal, Debasattam
Format: Article
Language:English
Subjects:
Chebyshev approximation
Complexity theory
Delays
Digital filters
Filter design (mathematics)
Filtering theory
Group delay
IIR filters
Interpolation
Mathematical model
Optimization
Signal processing
Temperature
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Summary:Obtaining a rational all-pass filter that matches a target phase response is a common problem in signal processing. Typical approaches have generally focused on optimizing filter coefficients while minimizing the deviation from the target phase response. However, these approaches typically do not offer a guarantee of exact match of the phase or any conditions on group delay. In this letter, we propose a Blaschke interpolation based all-pass filter design, wherein, if the phase response is known at n distinct frequencies, an all-pass filter that exactly satisfies the target values can be obtained. Moreover, the group delay at the interpolating points can be optimized or tuned to control the phase response for remaining frequencies. Simulations reveal that the design method is able to produce filters that closely match the target phase response accurately with much lower complexity than prior approaches.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2020.2965318