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Next: Gaussian Chirplet Up: The Chirplet Transform: Previous: Overview

THE CHIRPLET

The STFT consists of a correlation of the signal with constant-size portions of a wave, while the wavelet transform consists of correlations with a constant-Q family of functions. The two transforms, however, are in some ways similar. Although the former is generally thought of as a time-frequency method, and the latter, a time-scale method, both attempt to localize the signal in the time-frequency plane. In a rather loose sense, both the modulated window of the STFT, and the waveletgif of the wavelet transform, may be regarded as ``portions of waves''. Chirplets, in a similar manner, may be regarded as ``portions of chirps''. We generally use complex-valued chirplets to avoid the mirroring in the f=0 axis that results from using only real-valued chirplets.

Figure 2 provides a comparison in terms of real and imaginary components as well as time-frequency distributions, between a wave, wavelet, chirp, and chirplet.

  
Figure: FIGURE GOES SOMEWHERE IN THIS GENERAL VICINITY

In Fig. 3, we provide the same comparison with a 3-D particle-rendering, where the three coordinate axes are the function's real value, imaginary value, and time. Discrete samplings of four chirplets are shown: the top two have chirprate set to zero, and the leftmost two have an arbitrarily large window.

  
Figure: FIGURE GOES SOMEWHERE IN THIS GENERAL VICINITY





Steve Mann
Thu Jan 8 19:50:27 EST 1998