Fast Algorithms for Digital Computation of Linear Canonical Transforms

2016-01-01
Koc, Aykut
Öktem, Sevinç Figen
Ozaktas, Haldun M.
Kutay, M. Alper
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 approach is to define a discrete LCT (DLCT), based on which a fast LCT (FLCT) is derived to efficiently compute LCTs. This strategy is similar to that employed for the Fourier transform, where one defines the discrete Fourier transform (DFT), which is then computed with the fast Fourier transform (FFT). A third, hybrid approach involves a DLCT but employs a decomposition-based method to compute it. Algorithms for two-dimensional and complex parametered LCTs are also discussed.
LINEAR CANONICAL TRANSFORMS: THEORY AND APPLICATIONS

Suggestions

Digital computation of linear canonical transforms
Koc, Aykut; Ozaktas, Haldun M.; Candan, Çağatay; KUTAY, M. Alper (2008-06-01)
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...
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...
Efficient and Accurate Electromagnetic Optimizations Based on Approximate Forms of the Multilevel Fast Multipole Algorithm
Onol, Can; Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2016-01-01)
We present electromagnetic optimizations by heuristic algorithms supported by approximate forms of the multilevel fast multipole algorithm (MLFMA). Optimizations of complex structures, such as antennas, are performed by considering each trial as an electromagnetic problem that can be analyzed via MLFMA and its approximate forms. A dynamic accuracy control is utilized in order to increase the efficiency of optimizations. Specifically, in the proposed scheme, the accuracy is used as a parameter of the optimiz...
An evolutionary algorithm for multiple criteria problems
Soylu, Banu; Köksalan, Murat; Department of Industrial Engineering (2007)
In this thesis, we develop an evolutionary algorithm for approximating the Pareto frontier of multi-objective continuous and combinatorial optimization problems. The algorithm tries to evolve the population of solutions towards the Pareto frontier and distribute it over the frontier in order to maintain a well-spread representation. The fitness score of each solution is computed with a Tchebycheff distance function and non-dominating sorting approach. Each solution chooses its own favorable weights accordin...
Efficient analysis of phased arrays of microstrip patches using a hybrid generalized forward backward method/Green's function technique with a DFT based acceleration algorithm
Bakir, Onur; Aydın Çivi, Hatice Özlem; Erturk, Vakur B.; Chou, Hsi-Tseng (Institute of Electrical and Electronics Engineers (IEEE), 2008-6)
A hybrid method based on the combination of generalized forward backward method (GFBM) and Green's function for the grounded dielectric slab together with the acceleration of the combination via a discrete Fourier transform (DFT) based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation/scattering from electrically large, irregularly contoured two-dimensional arrays consisting of finite number of probe-fed microstrip patches. In this method, unknown current coefficien...
Citation Formats
A. Koc, S. F. Öktem, H. M. Ozaktas, and M. A. Kutay, “Fast Algorithms for Digital Computation of Linear Canonical Transforms,” LINEAR CANONICAL TRANSFORMS: THEORY AND APPLICATIONS, pp. 293–327, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46855.