Time-Frequency Based Instantaneous Frequency Estimation of Sparse Signals from an Incomplete Set of Samples

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Authors
  1. Orovic, I.
  2. Stankovic, S.
  3. Thayaparan, T.
Corporate Authors
Defence Research and Development Canada, Ottawa Research Centre, Ottawa ON (CAN)
Abstract
The estimation of time-varying instantaneous frequency for monocomponent signals with incomplete set of samples is considered. A suitable time-frequency distribution reduces the nonstationary signal into a local sinusoid over the lag variable prior to Fourier transform. Accordingly, the observed spectral content becomes sparse and suitable for compressive sensing reconstruction in the case of missing samples. Although the local bilinear or higher order autocorrelation functions will increase the number of missing samples, the analysis shows that accurate instantaneous frequency estimation can be achieved even if we deal with only few samples, as long as the auto-correlation function is properly chosen to coincide with signal’s phase non-linearity. Additionally, by employing the sparse signal reconstruction algorithms, the ideal time-frequency representations are obtained. The presented theory is illustrated on several examples dealing with different auto-correlation functions and corresponding time-frequency distributions.
Keywords
instantaneous frequency;time-frequency distributions;signal sparsity;autocorrelation function;reconstruction algorithms;orthogonal matching pursuit
Report Number
DRDC-RDDC-2014-P12 — External Literature
Date of publication
17 Jun 2014
Number of Pages
17
DSTKIM No
CA039226
CANDIS No
800027
Format(s):
Electronic Document(PDF)

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