A joint fractional domain signal representation is proposed based on an intuitive understanding from a time-frequency distribution of signals that designates the joint time and frequency energy content. The joint fractional signal representation (JFSR) of a signal is so designed that its projections onto the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR, including its relations to quadratic time-frequency representations and fractional Fourier transformations, which include the oblique projections of the JFSR. We present a fast algorithm to compute radial slices of the JFSR and the results are shown for various signals at different fractionally ordered domains.
© 2008 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: August 3, 2007
Revised Manuscript: December 19, 2007
Manuscript Accepted: January 9, 2008
Published: February 21, 2008
Lutfiye Durak, Ahmet Kemal Özdemir, and Orhan Arikan, "Efficient computation of joint fractional Fourier domain signal representation," J. Opt. Soc. Am. A 25, 765-772 (2008)