4,815 research outputs found
Integral representations of affine transformations in phase space with an application to energy localization problems
Applying the fractional Fourier transform and the Wigner distribution on a signal in a cascade fashion is equivalent with a rotation of the time and frequency parameters of the Wigner distribution. This report presents a formula for all unitary operators that are related to energy preserving transformations on the parameters of the Wigner distribution by means of such a cascade of operators. Furthermore, such operators are used to solve certain type of energy localization problems via the Weyl correspondence
Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms
Cataloged from PDF version of article.A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing
Chirp filtering in the fractional Fourier Domain
Cataloged from PDF version of article.In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta
function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of
the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as additive noise, the
FRT is used for filtering the line delta function in the appropriate fractional Fourier domain.
Experimental filtering results for a Gaussian input function, which is modulated by an additive chirp noise, are shown. Excellent agreement between experiments and computer simulations is achieved
Acoustic Seabed Classification using Fractional Fourier Transform
In this paper we present a time-frequency approach for acoustic seabed classification. Work reported is based on sonar data collected by the Volume Search Sonar (VSS), one of the five sonar systems in the AN/AQS-20. The Volume Search Sonar is a beamformed multibeam sonar system with 27 fore and 27 aft beams, covering almost the entire water volume (from above horizontal, through vertical, back to above horizontal). The processing of a data set of measurement in shallow water is performed using the Fractional Fourier Transform algorithm in order to determine the impulse response of the sediment. The Fractional Fourier transform requires finding the optimum order of the transform that can be estimated based on the properties of the transmitted signal. Singular Value Decomposition and statistical properties of the Wigner and Choi-Williams distributions of the bottom impulse response are employed as features which are, in turn, used for classification. The Wigner distribution can be thought of as a signal energy distribution in joint time-frequency domain. Results of our study show that the proposed technique allows for accurate sediment classification of seafloor bottom data. Experimental results are shown and suggestions for future work are provided
Phase space tomography reconstruction of the Wigner distribution for optical beams separable in Cartesian coordinates
We propose a simple approach for the phase space tomography reconstruction of the Wigner distribution of paraxial optical beams separable in Cartesian coordinates. It is based on the measurements of the antisymmetric fractional Fourier transform power spectra, which can be taken using a flexible optical setup consisting of four cylindrical lenses. The numerical simulations and the experimental results clearly demonstrate the feasibility of the proposed scheme
Optical transformation from chirplet to fractional Fourier transformation kernel
We find a new integration transformation which can convert a chirplet
function to fractional Fourier transformation kernel, this new transformation
is invertible and obeys Parseval theorem. Under this transformation a new
relationship between a phase space function and its Weyl-Wigner quantum
correspondence operator is revealed.Comment: 3 pages, no figur
High resolution time frequency representation with significantly reduced cross-terms
A novel algorithm is proposed for efficiently smoothing the slices of the Wigner distribution by exploiting the recently developed relation between the Radon transform of the ambiguity function and the fractional Fourier transformation. The main advantage of the new algorithm is its ability to suppress cross-term interference on chirp-like auto-components without any detrimental effect to the auto-components. For a signal with N samples, the computational complexity of the algorithm is O(N log N) flops for each smoothed slice of the Wigner distribution
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