A method for constructing orthonormal basis functions with good time-frequency localization

Izidor Gertner

doi:10.1117/12.2021282

3 June 2013 A method for constructing orthonormal basis functions with good time-frequency localization

Izidor Gertner

Proceedings Volume 8744, Automatic Target Recognition XXIII; 87440W (2013) https://doi.org/10.1117/12.2021282
Event: SPIE Defense, Security, and Sensing, 2013, Baltimore, Maryland, United States

Abstract

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.

Citation Download Citation

Izidor Gertner "A method for constructing orthonormal basis functions with good time-frequency localization", Proc. SPIE 8744, Automatic Target Recognition XXIII, 87440W (3 June 2013); https://doi.org/10.1117/12.2021282

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