Abstract
The real cepstrum is used to design an arbitrary length minimum-phase finite-impulse response filter from a mixed-phase prototype. There is no need to start with the odd-length equiripple linear-phase filter first. Neither the phase-unwrapping nor root-finding procedure is needed. Only two fast Fourier transforms and a recursive procedure are required to find the filter's impulse response from its real cepstrum. The resulting filter's magnitude response is exactly the same as the original one even when the filter is of very high order
Highlights
I N MANY low-delay applications of finite-impulse response (FIR) filter design such as data communication system, linear-phase characteristic is not necessary, and minimum-phase design can preserve the desired magnitude response and has the advantage of minimum delay over other counterparts with the same magnitude response.Many methods have been developed to design minimum-phase FIR filters, especially the one proposed by Herrmann and Schuessler [1]
It starts with an odd-length linear-phase equiripple FIR filter and shifts it up by one-half the stopband’s peak-to-peak ripple, which results in second-order zeros on the unit circle
The resultant minimum-phase filter magnitude response will be exactly the same as the original one even when the filter is of high order
Summary
I N MANY low-delay applications of finite-impulse response (FIR) filter design such as data communication system, linear-phase characteristic is not necessary, and minimum-phase design can preserve the desired magnitude response and has the advantage of minimum delay over other counterparts with the same magnitude response. A different approach based on root moments was proposed to design minimum-phase FIR filters [5] that preserve the same magnitude response. It needs to start from a linear-phase FIR filter due to the complex conjugate relation between its zeros. From the previous works of Mian and Nainer [2], we can extend it and avoid phase unwrapping by using real cepstrum This benefits from the problem itself, that is, constructing the minimum-phase counterpart from its magnitude.
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