In this paper we derive an explicit, single expression for a complex-valued, orthonormal basis well localized in time-frequency domain. We construct it from a single real function Φ(x) which is a Gaussian divided by the square root of a Jacobi theta θ₃ function. Then we simplify Φ(x) to the form of inverse square root of a Jacobi theta θ₃ function. We show that the shape of Φ(x) can be changed from Gaussian-like to rectangular-like with a single parameter. The basis generating function Φ(x) and its Fourier transform Φ have exponential decay. We also show how to modify a standard I and Q processor to compute complex-valued time-frequency expansion coefficients.

Date Published: 3 June 2013
PDF: 14 pages
Proc. SPIE 8744, Automatic Target Recognition XXIII, 87440W (3 June 2013); doi: 10.1117/12.2021282

Published in SPIE Proceedings Vol. 8744:
Automatic Target Recognition XXIII
Firooz A. Sadjadi; Abhijit Mahalanobis, Editor(s)