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 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 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.
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.