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The discrete fractional Fourier transform based on the DFT matrix

Signal Processing, 2011
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Lütfiye Durak Ata, Ahmet Serbes
exaly   +6 more sources

The discrete fractional Fourier transform [PDF]

IEEE Transactions on Signal Processing, 2000
We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier ...
Cagatay Candan, H M Ozaktas, M A Kutay
exaly   +5 more sources

Steerable Discrete Fourier Transform [PDF]

IEEE Signal Processing Letters, 2017
Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform (DFT), called steerable DFT (SDFT ...
Giulia Fracastoro, Enrico Magli
exaly   +2 more sources

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Time-frequency scaling property of Discrete Fourier Transform (DFT)

2010 IEEE International Conference on Acoustics, Speech and Signal Processing, 2010
This paper presents the analogue of the time or frequency scaling theorem of continuous time/frequency Fourier Transform (FT) to the realm of Discrete Fourier Transform (DFT). The scaling property applies to scaling by integers which are relatively prime to the length of the DFT. The time reversal property of DFT is identified as a special case of this
Sumit A Talwalkar
exaly   +2 more sources

Eigenvectors and functions of the discrete Fourier transform

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1982
-A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT.
B Dickinson, K Steiglitz
exaly   +1 more source

Eigenvectors of the DFT and discrete fractional fourier transform based on the bilinear transform

2010 IEEE 18th Signal Processing and Communications Applications Conference, 2010
Orthonormal eigenvectors of the DFT matrix, which is closer to the samples of Hermite-Gaussian functions, are crucial to define the discrete fractional Fourier transform. In this work we determine the eigenvectors of the DFT matrix inspired by the bilinear transform.
Lütfiye Durak Ata, Ahmet Serbes
exaly   +2 more sources

Discrete Fourier Transforms: DtFT and DFT

2021
In this chapter we investigate a big family of Fourier transforms: continuous Fourier transform (CFT), Fourier series (FS), discrete-time Fourier transform (DtFT), and discrete Fourier transform (DFT). The DFT, in its fast form (FFT), is probably one of the most frequently used orthogonal transforms in the world apart from the discrete cosine transform
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High-resolution spectral analysis (HSA) vs. discrete fourier transform (DFT)

INTER-NOISE and NOISE-CON Congress and Conference Proceedings, 2021
The Discrete Fourier Transform (DFT) is the standard technique for performing spectral analysis. It is used in the form of the well-known fast implementation (FFT) in almost all areas that deal with signal processing. However, the DFT algorithm has some limitations in terms of its resolution in time and frequency: the higher the time resolution, the ...
Roland Sottek, Thiago Lobato
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Flexible systolic design with asynchronous communication protocols for discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT)

SPIE Proceedings, 1994
ABSTRACT In this paper, a spiral systolic array (SA) architecture with asynchronous controls forthe real time realization of an N point DFT and [DFT is considered. The study includes theoverall system block diagram, propagation of data between array PEs, operations withineach PE, and the PE protocol for computing an N point DFT.
Kamran Reihani, Wiley E. Thompson, Yiping Fan   +2 more
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