Fast and accurate linear canonical transform algorithms
Author
Özaktaş, Haldun M.
Koç, A.
Date
2015Source Title
Proceedings of the 23nd Signal Processing and Communications Applications Conference, SIU 2015
Publisher
IEEE
Pages
1409 - 1412
Language
Turkish
Type
Conference PaperItem Usage Stats
159
views
views
145
downloads
downloads
Abstract
Linear canonical transforms are encountered in many areas of science and engineering. Important transformations such as the fractional Fourier transform and the ordinary Fourier transform are special cases of this transform family. This family of transforms is especially important for the modelling of wave propagation. It has many applications such as noise removal, image encryption, and analysis of optical systems. Here we discuss algorithms for fast and accurate computation of these transforms. These algorithms can achieve the same accuracy and speed as fast Fourier transform algorithms, so that they can be viewed as optimal algorithms. Efficient sampling of signals plays an important part in the development of these algorithms.
Keywords
ABCD opticsTransforms
Digital signal processing
Eigenvalues and eigenfunctions
Fast Fourier transforms
Fourier optics
Importance sampling
Optical systems
Signal processing
Wave propagation
Accurate computations
Efficient sampling
Fast algorithms
Fast Fourier transform algorithm
Linear canonical transform
Quadratic phase systems
Science and engineering
Mathematical transformations
Permalink
http://hdl.handle.net/11693/28330Published Version (Please cite this version)
http://dx.doi.org/10.1109/SIU.2015.7130106Collections
Related items
Showing items related by title, author, creator and subject.
-
Sparse representation of two-and three-dimensional images with fractional fourier, hartley, linear canonical, and haar wavelet transforms
Koç A.; Bartan, B.; Gundogdu, E.; Çukur, T.; Haldun M. Özaktaş (Elsevier Ltd, 2017)Sparse recovery aims to reconstruct signals that are sparse in a linear transform domain from a heavily underdetermined set of measurements. The success of sparse recovery relies critically on the knowledge of transform ... -
miR-200c: a versatile watchdog in cancer progression, EMT, and drug resistance
Mutlu, M.; Raza, U.; Saatci, Ö.; Eyüpoğlu, E.; Yurdusev, E.; Şahin, Ö. (Springer Verlag, 2016-06)MicroRNAs (miRNAs) are 20–22-nucleotide small endogenous non-coding RNAs which regulate gene expression at post-transcriptional level. In the last two decades, identification of almost 2600 miRNAs in human and their potential ... -
Linear canonical transforms, degrees of freedom, and sampling in optical signals and systems
Özaktaş, Haldun M.; Öktem, F. S. (IEEE, 2014)We study the degrees of freedom of optical systems and signals based on space-frequency (phase-space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency ...