Estimating the length of a compact function from a noisy measurement of the modulus of its Fourier transform

1 December 1965

journal article
Published by Institution of Engineering and Technology (IET) in Electronics Letters

Vol. 1 (10) , 279
https://doi.org/10.1049/el:19650253

Abstract

Consider f, zero outside an interval of length L, and its Fourier transform F. It is known that, if arg F is unknown, L can be found from (a) the Fourier transform of |F|² or (b) the Fourier transform of |F| exp(jϕ), where ϕ = Hilbert transfrom of In|F|. It appears that method (b) may be superior if |F| is measured in the presence of noise.

Keywords

MATHEMATICS
MEASUREMENT
NOISE

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