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Zak transform and a new approach to waveform design

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1 Author(s)
Gladkova, I. ; Dept. of Comput. Sci., City Coll. of New York, NY, USA

The ambiguity function Af (τ, v) of a transmitted signal f(t) measures the uncertainty with which the returning echo distinguishes, simultaneously, both ranges and velocities of a target system. Generally speaking, Af (τ, v) is desired to be of "thumbtack" shape, i.e., a function whose absolute value has a graph with a strong peak at the origin over a broad shallow base. The ambiguity function can be computed directly from the Zak transform Zf (x,y) of the signal f(t), so waveforms with desirable ambiguity functions can be designed in the Zak domain. In the Zak domain, computation of Af (τ, v) on the integer lattice is exceptionally simple, particularly for pulse train signals. For a pulse train, the Zak transform is obtained by multiplying the Zak transform of a rectangular pulse of duration 1 by a multivariate trigonometric polynomial whose coefficients are the coefficients defining the pulse train. Reversing this observation, one can start with such a trigonometric polynomial and construct a pulse train signal. We propose a systematic method for constructing such waveforms, which we illustrate in a particular case

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Aerospace and Electronic Systems, IEEE Transactions on  (Volume:37 ,  Issue: 4 )