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Advisor(s)
Abstract(s)
In this work we propose a method based on compressive sensing (CS)
for estimating the spectrum of a signal written as a linear combination of a small
number of sinusoids. In practice one deals with signals with finite-length and so
the Fourier coefficients are not exactly sparse. Due to the leakage effect in the case
where the frequency is not a multiple of the fundamental frequency of the DFT, the
success of the traditional CS algorithms is limited. To overcome this problem our
algorithm transform the DFT basis into a frame with a larger number of vectors, by
inserting a small number of columns between some of the initial ones. The
algorithm takes advantage of the compactness of the interpolation function that
results from the ‘1 norm minimization of the Basis Pursuit (BP) and is based on the
compressive sensing theory that allows us to acquire and represent sparse and
compressible signals, using a much lower sampling rate than the Nyquist rate. Our
method allow us to estimate the sinusoids amplitude, phase and frequency.
Description
Keywords
Basis Pursuit Compressive sensing Interpolating function Redundant frames Sparse representations Spectral estimation
Citation
Publisher
Springer Netherlands