An algebraic approach to discrete short-time Fourier transform analysis and synthesis

Shpiro, Z.; Malah, D.

doi:10.1109/icassp.1984.1172422

Cited by 12 publications

(4 citation statements)

References 9 publications

(12 reference statements)

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“…For an irregular scanning locus, it may not be trivial to estimate accurately its derivative. For example, in our x-ray microtomographic study, the scanning locus is subject to random interferences introduced by the mechanical rotation of the specimen stage [11]- [13]. As a result, a precise estimation of the derivative of the scanning locus is particularly difficult.…”

Section: Discussionmentioning

confidence: 99%

“…As a result, a precise estimation of the derivative of the scanning locus is particularly difficult. On the other hand, the practical scanning locus used in x-ray microtomography can be made to meet our three conditions [11]- [13]. Without using the derivative of the scanning locus, the proposed formula will not be affected by the error in estimating the derivative.…”

Section: Discussionmentioning

confidence: 99%

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A derivative-free noncircular fan-beam reconstruction formula

Wang¹,

Lin²,

Cheng³

1993

IEEE Trans. on Image Process.

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In order to perform fan-beam reconstruction using projection data collected from a noncircular scanning locus, existing noncircular fan-beam formulas require a derivative of the scanning locus with respect to the rotation angle. A derivative-free noncircular fan-beam reconstruction formula that is based on a geometrical explanation of the circular equispatial fan-beam reconstruction formula is obtained here. A mathematical proof is then provided under the conditions that the source-to-origin distance is symmetric with respect to the origin of the reconstruction coordinate system, is differentiable almost everywhere, and does not change too fast with respect to the rotation angle. The derivative-free noncircular fan-beam reconstruction formula is the same as the circular one, except that the source-to-origin distance is a function of the rotation angle. A typical simulation result for the noncircular fan-beam formula is given.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

A derivative-free noncircular fan-beam reconstruction formula

Wang¹,

Lin²,

Cheng³

1993

IEEE Trans. on Image Process.

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“…However, Shpiro and Malah [6] showed that those definitions can be extended to the discrete Fourier transform. Therefore, we present definitions of the reconstruction techniques here that are based on the discrete STFT.…”

Section: Signal Reconstructionmentioning

confidence: 99%

“…Griffin and Lim [3] and Shpiro and Malah [6] show that the following signal reconstruction from the MSTFT minimizes the distance measure [ ( ), …”

Section: Signal Reconstructionmentioning

confidence: 99%

Analysis of signal reconstruction after modulation filtering

Schimmel

Atlas

2005

Advanced Signal Processing Algorithms, Architectures, and Implementations XV

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When the short-time Fourier transform (STFT) of an audio signal is arbitrarily modified, it no longer truly represents a time-domain signal. Classically, the accepted solution to obtain a time-domain signal from a modified STFT (MSTFT) is to invert the MSTFT to a time-domain signal that has an STFT that is closest to the MSTFT in a least squares sense. This is also the approach currently taken by our modulation filtering techniques. However, it was never established that using the original and unmodified STFT phase in this reconstruction is optimal for modulation filtering. In this paper, we compare our signal reconstruction approach to a well-known iterative procedure that approximates a time-domain signal using only the STFT magnitude. We analyze the signal reconstruction of speech signals after filtering them with low-pass, band-pass and high-pass modulation filters. Our study shows that the iterative procedure yields quantitatively and qualitatively comparable signals at significantly higher computational cost. It therefore does not seem a worthwhile alternative to our current reconstruction technique, but it may prove useful for IIR modulation filtering.

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The legality problem of linear systems in Gabor time-frequency space

Farkash

Raz

1993

Signal Processing

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An algebraic approach to discrete short-time Fourier transform analysis and synthesis

Cited by 12 publications

References 9 publications

A derivative-free noncircular fan-beam reconstruction formula

A derivative-free noncircular fan-beam reconstruction formula

Analysis of signal reconstruction after modulation filtering

The legality problem of linear systems in Gabor time-frequency space

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