Design of Allpass Fractional Delay Filter and Fractional Hilbert Transformer Using Closed-Form of Cepstral Coefficients

Pei, Soo‐Chang; Lin, Huei-Shan; Wang, Penghua

doi:10.1109/iscas.2007.378367

Cited by 8 publications

(8 citation statements)

References 11 publications

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“…Similar to the results in [8], the scaling property facilitates update of the filter coefficients corresponding to different delay value and phase shift. Only the two normalized complexcepstrum sequences need to be calculated once and stored.…”

Section: Criterion Formulation and Closed-form Solutionmentioning

confidence: 77%

“…This filter can be applied to deal with the problem of adaptive sub-sample delay estimation [21], which employs a quadrature detector based on Hilbert transform filtering and delaying the input signal by a fractional amount of the sample period. In this paper, we extend the result of [8], simultaneously considering the criteria of phase and group delay at midband frequency (π/2) to obtain explicit formula of the complex cepstrum for a fractional delay fractional Hilbert transformer (FDFHT). The result reveals that the complex cepstrum is proportional to the design parameters-the FD and the fractional phase shift.…”

Section: Introductionmentioning

confidence: 93%

“…The design of IIR FD filter, on the other hand, can be traced back to [7], in which an allpole filter is proposed with MF group delay response at the DC frequency. Alternatively, we can also design an FD filter as an IIR allpass system since only the phase information is concerned [8] [9].…”

Section: Introductionmentioning

confidence: 99%

“…In [8], the authors apply the MF condition in phase/group-delay response to derive the explicit formula of complex/differential cepstrum for IIR allpass FD filters and FHT. [9] extends the results of FD filter design to FIR types and proposes two tunable structures for implementation of FIR/IIR FD filters.…”

Section: Introductionmentioning

confidence: 99%

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Design of IIR allpass fractional-delay fractional Hilbert transformer using complex cepstrum

Pei

Lin

2010

Proceedings of 2010 IEEE International Symposium on Circuits and Systems

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The IIR allpass fractional-delay fractional Hilbert transformer is designed in the complex-cepstrum domain. The maximal flatness criterion on the phase response is considered for the midband frequency. Two independent systems of linear equations are formulated, resulting in closed-form solutions of the even-index and odd-index parts of complex cepstrum of the denominator polynomial. Moreover, they are proportional to the two design parameters: fractional delay and phase shift. This is attractive in that a tunable scheme for variable parameters is realizable. Only two normalized complex-cepstrum sequences need to be designed, stored and tuned by scaling. Both nonrecursive and recursive algorithms are available for renewing the filter coefficients from the complex cepstrum.

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Section: Criterion Formulation and Closed-form Solutionmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design of IIR allpass fractional-delay fractional Hilbert transformer using complex cepstrum

Pei

Lin

2010

Proceedings of 2010 IEEE International Symposium on Circuits and Systems

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“…The direct approach is usually taken in the design of all-pass transformers. Popular methods for their design are based on the eigenvalue problem [5], maximally flat [6], [7] and least pth phase-error criterion [8], fractional differencing [9], and the Peano kernel [10]. These methods result in causal transformers.…”

Section: T He Fractional Hilbert Transform Was Introduced Bymentioning

confidence: 99%

Noncausal IIR Fractional Hilbert Transformers With Equiripple or Flat Phase Response

Molnar

Vučić

2010

IEEE Trans. Circuits Syst. II

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Noncausal infinite impulse response (IIR) systems yield a much better approximation of desired response than causal systems of the same complexity. Today's technology also enables their efficient implementation. In the design of Hilbert transformers, the noncausal approach has been exploited only for conventional transformers. This brief presents a method for the design of noncausal IIR fractional Hilbert transformers based on the elliptic approximation of the desired phase shift. All-pass transformers with equiripple and flat phase responses are considered. The method is given in closed form, which makes the design robust and suitable for high-order transformers.Index Terms-All-pass system, elliptic approximation, equiripple phase, flat phase, fractional Hilbert transformer (FHT), noncausal infinite impulse response (IIR) system.

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Design of discrete Fractional Hilbert transformer in time domain

Pei¹,

Wang

Lin

2008

2008 IEEE International Symposium on Circuits and Systems (ISCAS)

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Design of Allpass Fractional Delay Filter and Fractional Hilbert Transformer Using Closed-Form of Cepstral Coefficients

Cited by 8 publications

References 11 publications

Design of IIR allpass fractional-delay fractional Hilbert transformer using complex cepstrum

Design of IIR allpass fractional-delay fractional Hilbert transformer using complex cepstrum

Noncausal IIR Fractional Hilbert Transformers With Equiripple or Flat Phase Response

Design of discrete Fractional Hilbert transformer in time domain

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