Digital computation of linear canonical transforms

Download
2008-06-01
Koc, Aykut
Ozaktas, Haldun M.
Candan, Çağatay
KUTAY, M. Alper
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 log N time, where N is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.
IEEE TRANSACTIONS ON SIGNAL PROCESSING

Suggestions

Fast Algorithms for Digital Computation of Linear Canonical Transforms
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...
Linear Algebraic Analysis of Fractional Fourier Domain Interpolation
Öktem, Sevinç Figen (2009-01-01)
n this work, we present a novel linear algebraic approach to certain signal interpolation problems involving the fractional Fourier transform. These problems arise in wave propagation, but the proposed approach to these can also be applicable to other areas. We see this interpolation problem as the problem of determining the unknown signal values from the given samples within some tolerable error We formulate the problem as a linear system of equations and use the condition number as a measure of redundant ...
Fine resolution frequency estimation from three DFT samples: Case of windowed data
Candan, Çağatay (2015-09-01)
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.
Efficient Computation of Green's Functions for Multilayer Media in the Context of 5G Applications
Mittra, Raj; Özgün, Özlem; Li, Chao; Kuzuoğlu, Mustafa (2021-03-22)
This paper presents a novel method for effective computation of Sommerfeld integrals which arise in problems involving antennas or scatterers embedded in planar multilayered media. Sommerfeld integrals that need to be computed in the evaluation of spatial-domain Green's functions are often highly oscillatory and slowly decaying. For this reason, standard numerical integration methods are not efficient for such integrals, especially at millimeter waves. The main motivation of the proposed method is to comput...
Fixed-frequency slice computation of discrete Cohen's bilinear class of time-frequency representations
Ozgen, MT (2000-02-01)
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...
Citation Formats
A. Koc, H. M. Ozaktas, Ç. Candan, and M. A. KUTAY, “Digital computation of linear canonical transforms,” IEEE TRANSACTIONS ON SIGNAL PROCESSING, pp. 2383–2394, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/33400.