242,133 research outputs found
Steerable Discrete Fourier Transform
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, called steerable
DFT (SDFT). Since the DFT is used in numerous fields, it may be of interest in
a wide range of applications. Moreover, we also show that the SDFT is highly
related to other well-known transforms, such as the Fourier sine and cosine
transforms and the Hilbert transforms
Fast complexified quaternion Fourier transform
A discrete complexified quaternion Fourier transform is introduced. This is a
generalization of the discrete quaternion Fourier transform to the case where
either or both of the signal/image and the transform kernel are complex
quaternion-valued. It is shown how to compute the transform using four standard
complex Fourier transforms and the properties of the transform are briefly
discussed
On the diagonalization of the discrete Fourier transform
The discrete Fourier transform (DFT) is an important operator which acts on
the Hilbert space of complex valued functions on the ring Z/NZ. In the case
where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors
for the DFT. The transition matrix from the standard basis to the canonical
basis defines a novel transform which we call the discrete oscillator transform
(DOT for short). Finally, we describe a fast algorithm for computing the
discrete oscillator transform in certain cases.Comment: Accepted for publication in the journal "Applied and Computational
Harmonic Analysis": Appl. Comput. Harmon. Anal. (2009),
doi:10.1016/j.acha.2008.11.003. Key words: Discrete Fourier Transform, Weil
Representation, Canonical Eigenvectors, Oscillator Transform, Fast Oscillator
Transfor
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