TY - GEN

T1 - Doǧrusal kanoni̇k dönüşümünün özfonksi̇yonlari

AU - Serbes, Ahmet

AU - Aldirmaz, Sultan

AU - Durak-Ata, Lütfiye

PY - 2012

Y1 - 2012

N2 - The linear canonical transform (LCT) is a powerful tool for signal processing applications and is also the generalized form of the well-known transforms such as Fourier, fractional Fourier and Fresnel transforms, and some operators such as scaling, chirp multiplication and chirp convolution. The LCT is characterized by a 2 x 2 unit-determinant matrix of parameters {a, b, c, d}. When studying linear operators, one of the crucial steps in order to understand what the operators do, is to find their eigenfunctions. Eigenfunctions of the LCT may be useful for applications such as self-imaging and resonance problems. In this paper, we derive eigenfunctions of the LCT for different cases. In order to expose eigenfunctions of the LCT, we split our investigation into three parts: (a + d) > 2, (a + d) < -2, and |a+d| < 2. The complete set of eigenfunctions is known to be chirp functions modulated by scaled harmonic oscillator (also known as Hermite-Gaussian) functions for the case |a+d| < 2. However, we propose that when |a + d| > 2, the eigenfunction set of the LCT are chirp functions modulated with imaginary-width Hermite polynomials.

AB - The linear canonical transform (LCT) is a powerful tool for signal processing applications and is also the generalized form of the well-known transforms such as Fourier, fractional Fourier and Fresnel transforms, and some operators such as scaling, chirp multiplication and chirp convolution. The LCT is characterized by a 2 x 2 unit-determinant matrix of parameters {a, b, c, d}. When studying linear operators, one of the crucial steps in order to understand what the operators do, is to find their eigenfunctions. Eigenfunctions of the LCT may be useful for applications such as self-imaging and resonance problems. In this paper, we derive eigenfunctions of the LCT for different cases. In order to expose eigenfunctions of the LCT, we split our investigation into three parts: (a + d) > 2, (a + d) < -2, and |a+d| < 2. The complete set of eigenfunctions is known to be chirp functions modulated by scaled harmonic oscillator (also known as Hermite-Gaussian) functions for the case |a+d| < 2. However, we propose that when |a + d| > 2, the eigenfunction set of the LCT are chirp functions modulated with imaginary-width Hermite polynomials.

UR - http://www.scopus.com/inward/record.url?scp=84863469499&partnerID=8YFLogxK

U2 - 10.1109/SIU.2012.6204688

DO - 10.1109/SIU.2012.6204688

M3 - Konferans katkısı

AN - SCOPUS:84863469499

SN - 9781467300568

T3 - 2012 20th Signal Processing and Communications Applications Conference, SIU 2012, Proceedings

BT - 2012 20th Signal Processing and Communications Applications Conference, SIU 2012, Proceedings

T2 - 2012 20th Signal Processing and Communications Applications Conference, SIU 2012

Y2 - 18 April 2012 through 20 April 2012

ER -