Site Search:

The STFT consists of a correlation of the signal with constantsize portions of a wave, while the wavelet transform consists of correlations with a constantQ family of functions. The two transforms, however, are in some ways similar. Although the former is generally thought of as a timefrequency method, and the latter, a timescale method, both attempt to localize the signal in the timefrequency plane. In a rather loose sense, both the modulated window of the STFT, and the wavelet 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 complexvalued chirplets to avoid the mirroring in the f=0 axis that results from using only realvalued chirplets.
Figure 2 provides a comparison in terms of real and imaginary components as well as timefrequency 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 3D particlerendering, 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