Abstract
Variable-phase (VP) digital filter can change its phase response during the online digital-signal processing (DSP). This paper proposes a linear-programming (LP) method for designing a VP filter in the minimax error sense, i.e., the maximum phase error is minimised. The mathematical model used to approximate a desired VP response (VP specification) is an all-pass transfer function whose numerator and denominator have exactly the same coefficients. In this paper, we first derive a frequency-response error that is a non-linear function of the VP filter coefficients, and then approximate this frequency response as a linear function of the VP filter coefficients. Consequently, the minimax design of the VP filter reduces to a linear minimisation problem, which is solved through using an LP solver. We will use an example to demonstrate that the proposed LP-based VP design technique can obtain an all-pass VP filter with high accuracy. Moreover, the stability of the designed all-pass VP filter is also guaranteed.
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