One-dimensional and two-dimensional generalised discrete fourier transforms

Bongiovanni, G.; Corsini, Paolo; Frosini, Graziano

doi:10.1109/tassp.1976.1162764

Cited by 39 publications

(20 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is achieved by introducing an equation or (37) This equation implicitly defines the right boundary condition . Further, (37) determines the entire right signal extension obtained by reducing , , modulo : (38) Algebraically, the boundary condition replaces the vector space by the vector space , which is of the same dimension, but closed under multiplication by the time shift operator and thus a module. The corresponding algebra , generated by , is identical to .…”

Section: Boundary Conditions and Signal Extensionmentioning

confidence: 99%

“…Thus, the signal extension in both directions is determined by one (37), which provides the left and the right boundary condition: boundary condition right and left signal extension 11 A polynomial q(x) is invertible in By assuming the generic boundary condition , we obtain a valid signal model. However, the corresponding signal extension (38) has in general no simple structure. To obtain a module that is reasonable for applications, we thus require the following:…”

Section: Boundary Conditions and Signal Extensionmentioning

confidence: 99%

See 1 more Smart Citation

Algebraic Signal Processing Theory: Foundation and 1-D Time

Püschel

Moura

2008

IEEE Trans. Signal Process.

152

195

View full text Add to dashboard Cite

show abstract

Section: Boundary Conditions and Signal Extensionmentioning

confidence: 99%

Section: Boundary Conditions and Signal Extensionmentioning

confidence: 99%

Algebraic Signal Processing Theory: Foundation and 1-D Time

Püschel

Moura

2008

IEEE Trans. Signal Process.

152

195

View full text Add to dashboard Cite

show abstract

“…It is a particular case of the Generalized DFT [17]. Compared with the standard DFT, we see that it simply corresponds to shifting the frequency index by a factor 1/2.…”

Section: The Odd-frequency Dftmentioning

confidence: 94%

Separating time-frequency sources from time-domain convolutive mixtures using non-negative matrix factorization

Leglaive

Badeau

Richard

2017

2017 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA)

View full text Add to dashboard Cite

This paper addresses the problem of under-determined audio source separation in multichannel reverberant mixtures. We target a semiblind scenario assuming that the mixing filters are known. Source separation is performed from the time-domain mixture signals in order to accurately model the convolutive mixing process. The source signals are however modeled as latent variables in a time-frequency domain. In a previous paper we proposed to use the modified discrete cosine transform. The present paper generalizes the method to the use of the odd-frequency short-time Fourier transform. In this domain, the source coefficients are modeled as centered complex Gaussian random variables whose variances are structured by means of a non-negative matrix factorization model. The inference procedure relies on a variational expectation-maximization algorithm. In the experiments we discuss the choice of the source representation and we show that the proposed approach outperforms two methods from the literature.Index Terms-Audio source separation, reverberant mixtures, non-negative matrix factorization, variational inference.

show abstract

“…In [3], (one and two-dimensional) generalized DFT (GFT) was introduced and some basic properties were derived. In particular, it was shown that a given one-dimensional GFT on a vector v can be performed by means of an infinite number of two-dimensional GFTs on a matrix A whose elements are the elements of v properly ordered.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, it was shown that a given one-dimensional GFT on a vector v can be performed by means of an infinite number of two-dimensional GFTs on a matrix A whose elements are the elements of v properly ordered. In [6], multidimensional generalized DFT was introduced and its characteristics were investigated while some general results were derived that included as particular cases the properties previously given in [3].…”

Section: Introductionmentioning

confidence: 99%