Complex wavelet transforms with allpass filters

Fernandes, Felix C. A.; Selesnick, Ivan; Spaendonck, R.L.C. van; Burrus, C.S.

doi:10.1016/s0165-1684(03)00077-x

Cited by 66 publications

(30 citation statements)

References 37 publications

(48 reference statements)

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“…Furthermore we would like to point out that the redundancy of the dual-tree complex wavelet transform can be overcome by using the softy-space projection [10] which relieves the redundancy by projecting the real-valued image on a hypercomplex image of lower resolution.…”

Section: Resultsmentioning

confidence: 99%

Steerable Filters Generated with the Hypercomplex Dual-Tree Wavelet Transform

Wedekind

Amavasai

Dutton

2007

2007 IEEE International Conference on Signal Processing and Communications

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Section: Resultsmentioning

confidence: 99%

Steerable Filters Generated with the Hypercomplex Dual-Tree Wavelet Transform

Wedekind

Amavasai

Dutton

2007

2007 IEEE International Conference on Signal Processing and Communications

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“…These methods do have some fundamental differences. Time-domain methods [3], [8], [10] require the generation of filter coefficients, the analytic signal being obtained as the output of these filters. They are based on approximations to a continuous spectrum.…”

Section: Resultsmentioning

confidence: 99%

“…Other examples include discrete wavelet transforms, where we see a reduction of shift sensitivity and improved directionality [2] analysis [1], where they are used in the estimation of instantaneous frequency. Methods currently used to generate DTA signals are either time-domain [3], [8], [10] filtering methods or frequency-based ones [5], [7]. The former requires the generation of filter coefficients; the analytic signal is then obtained as the output of these filters.…”

Section: Introductionmentioning

confidence: 99%

A frequency-domain method for generation of discrete-time analytic signals

Elfataoui

Mirchandani

2006

IEEE Trans. Signal Process.

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Abstract-We consider a common frequency-domain procedure hilbert for generating discrete-time analytic signals and show how it fails for a specific class of signals. A new frequency-domain technique ehilbert is formulated that solves the defect. Moreover, the new technique is applicable to all discrete-time real signals of even length. It is implemented by the introduction of one additional zero of the continuous spectrum of the analytic signal hilbert at a negative frequency. Both frequency-domain methods generate equal length discrete-time analytic signals. The new analytic signal preserves the original signal (real part) and also the zeros of the discrete spectrum hilbert in the negative frequencies. The greater attenuation at the negative frequencies affects the degree of aliasing of the analytic signal. It is measured by applying the analytic signal to an orthogonal wavelet transform and determining the improved transform shiftability.

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“…The essential difference compared with the half-sample shifted CQF filter bank (Selesnick, 2002) is the linear phase of the BDWT bank and the FD B-spline filters adapted in this work. The shifted CQF filter bank is constructed with the aid of the all-pass Thiran filters and the scaling and wavelet coefficients suffer from nonlinear phase distortion effects (Fernandes, 2003). The linear phase warrants that the wavelet sequences in different scales are accurately time related.…”

Section: Discussionmentioning

confidence: 99%

“…Gopinath (2003) generalized the idea by introducing the M parallel CQFs, which have a fractional phase shift with each other. Both Selesnick and Gopinath have constructed the parallel CQF bank with the aid of the all-pass Thiran filters, which suffers from nonlinear phase distortion effects (Fernandes, 2003). In this book chapter we introduce a linear phase and shift invariant BDWT bank consisting of M fractionally delayed wavelets.…”

Section: Introductionmentioning

confidence: 99%