Fixed-frequency slice computation of discrete Cohen's bilinear class of time-frequency representations

Ozgen, MT
This communication derives DFT-sample-based discrete formulas directly in the spectral-correlation domain for computing fixed-frequency slices of discrete Cohen's class members with reduced computational cost, both for one-dimensional and multidimensional (specifically two-dimensional (2-D)) finite-extent sequence cases. Frequency domain integral expressions that define discrete representations are discretized to obtain these discrete implementation formulas. 2-D ambiguity function domain kernels are chosen to have separable forms for analytical convenience. Simulations demonstrating the DFT-sample-based computation in particle-location analysis of in-line Fresnel holograms are presented.


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Koc, Aykut; Öktem, Sevinç Figen; Ozaktas, Haldun M.; Kutay, M. Alper (2016-01-01)
Fast and accurate algorithms for digital computation of linear canonical transforms (LCTs) are discussed. Direct numerical integration takes O.N-2/time, where N is the number of samples. Designing fast and accurate algorithms that take O. N logN/time is of importance for practical utilization of LCTs. There are several approaches to designing fast algorithms. One approach is to decompose an arbitrary LCT into blocks, all of which have fast implementations, thus obtaining an overall fast algorithm. Another a...
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An efficient and low complexity frequency estimation method based on the discrete Fourier transform (DFT) samples is described. The suggested method can operate with an arbitrary window function in the absence or presence of zero-padding. The frequency estimation performance of the suggested method is shown to follow the Cramer-Rao bound closely without any error floor due to estimator bias, even at exceptionally high signal-to-noise-ratio (SNR) values.
Excessive Memory Usage of the ELLPACK Sparse Matrix Storage Scheme throughout the Finite Element Computations
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Sparse matrices are occasionally encountered during solution of various problems by means of numerical methods, particularly the finite element method ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage sche...
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We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take similar to N...
Citation Formats
M. Ozgen, “Fixed-frequency slice computation of discrete Cohen’s bilinear class of time-frequency representations,” SIGNAL PROCESSING, pp. 219–230, 2000, Accessed: 00, 2020. [Online]. Available: