Identification of Chirps with Continuous Wavelet Transform
Chirps are signals (or sums of signals) that may be characterized by a local (i.e. time-dependent) amplitude and a local frequency. Time-frequency representations such as wavelet representations are well adapted to the characterization problem of such chirps. Ridges in the modulus of the transform determine regions in the transform domain with a high concentration of energy, and are regarded as natural candidates for the characterization and the reconstruction of the original signal. A couple of algorithmic procedures for the estimation of ridges from the modulus of the (continuous) wavelet transform of one-dimensional signals are described, together with a new reconstruction procedure, using only information of the restriction of the wavelet transform to a sample of points from the ridge. This provides with a very efficient way to code the information contained in the signal.
KeywordsCost Function Instantaneous Frequency Continuous Wavelet Transform Noisy Signal Chirp Signal
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