Design of minimum-phase FIR digital filter through cepstrum

Reddy, G. Ravi Shankar

doi:10.1049/el:19860840

Cited by 9 publications

(8 citation statements)

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“…Hence in the limit where Q is infinite, time domain factorization is identical to spectral factorization, a known result from linear systems theory [16]. Define the residual error e of the non-linear equations above as (14) . .…”

Section: B An Approximate Minimum Phase Factor C Approxmentioning

confidence: 99%

“…The O-W equations have implications for the implementation of a minimum phase transformation on a digital computer. This was demonstrated by Kidambi and Antoniou in 2017 [11], and [11] presented results for the design of minimum phase finite impulse response (FIR) Chebyshev filters, reporting residual errors orders of magnitude smaller than those obtained through competing methods [12], [13], [14], [8]. In terms of computational requirements, the Hilbert transform and the cepstrum are both based on the discrete Fourier transform (DFT) 1 and require very long FFT's to obtain good FIR filter performance.…”

Section: Introductionmentioning

confidence: 99%

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On the Computation of a Minimum Phase Factor

Olivier¹,

Barnard²

2022

Preprint

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Section: B An Approximate Minimum Phase Factor C Approxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Computation of a Minimum Phase Factor

Olivier¹,

Barnard²

2022

Preprint

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“…If the filter order is small then ϵ is negligible as is the case for the filter shown in Table 1. But it will be shown 8 in Section 3 that ϵ > 0 even for a filter order of 24. Hence, it follows that the difference between regularisation and lifting comes down to the choice of ϵ. Regularisation requires (in general) ϵ > 0, while lifting [11,12] deploys ϵ = 0.…”

Section: Of 10 -mentioning

confidence: 99%

Minimum phase finite impulse response filter design

Olivier

Barnard

2022

IET Signal Processing

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The design of minimum phase finite impulse response (FIR) filters is considered. The study demonstrates that the residual errors achieved by current state-of-the-art design methods are nowhere near the smallest error possible on a finite resolution digital computer. This is shown to be due to conceptual errors in the literature pertaining to what constitutes a factorable linear phase filter. This study shows that factorisation is possible with a zero residual error (in the absence of machine finite resolution error) if the linear operator or matrix representing the linear phase filter is positive definite. Methodology is proposed able to design a minimum phase filter that is optimal-in the sense that the residual error is limited only by the finite precision of the digital computer, with no systematic error. The study presents practical application of the proposed methodology by designing two minimum phase Chebyshev FIR filters. Results are compared to state-of-the-art methods from the literature, and it is shown that the proposed methodology is able to reduce currently achievable residual errors by several orders of magnitude.

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“…Several design methodologies for the design of a Chebyshev minimum phase filter have been proposed. The literature can broadly be categorized as promoting minimum phase FIR filter design based on the Hilbert transform [7], explicit enumeration of the polynomial roots (root finding) [8,3], the complex cepstrum [9] and spectral factorization [10]. The Hilbert transform and the cepstrum are both based on the discrete Fourier transform (DFT) 2 and require very long FFT's to obtain good FIR filter performance.…”

Section: Introductionmentioning

confidence: 99%

On minimum phase transformation and filter design

Olivier¹,

Barnard²

2022

Preprint

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Minimum-phase finite impulse response filters are widely used in practice, and much research has been devoted to the design of such filters. However, for the important case of Chebyshev filters there is a curious mismatch between current best practice and well-established theoretical principles. The paper shows that this difference can be understood through analysis of the time-domain factorization of a suitable extended matrix. This analysis explains why the definition of a factorable linear phase filter must be revised. The time domain analysis of factorization suggests initial values leading to fast and accurate convergence of iterative algorithms for the design of minimum-phase finite impulse response filters. Numerical results are provided to demonstrate that a significant improvement in filter tap accuracy is obtained when the well-established theoretical principles are correctly applied to the design of minimum phase finite impulse response filters.

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Design of minimum-phase FIR digital filter through cepstrum

Cited by 9 publications

References 0 publications

On the Computation of a Minimum Phase Factor

On the Computation of a Minimum Phase Factor

Minimum phase finite impulse response filter design

On minimum phase transformation and filter design

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