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.

**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

- Gaussian Chirplet
- Notation
- Time-Frequency-Scale Volume
- Gaussian Chirplet Transform (GCT)
- Continuous Chirplet Transform (CCT)
- Multiple Mother Chirplets: The Prolate Chirplets
- Autochirplet and Cross Chirplet Transforms

Thu Jan 8 19:50:27 EST 1998