As discussed in §G.8.2, an interesting generalization of sinusoidal modeling is chirplet modeling. A chirplet is defined as a Gaussian-windowed sinusoid, where the sinusoid has a constant amplitude, but its frequency may be linearly ``sweeping.'' This definition arises naturally from the mathematical fact that the Fourier transform of a Gaussian-windowed chirp signal is a complex Gaussian pulse, where a chirp signal is defined as a sinusoid having linearly modulated frequency, i.e., quadratic phase:
(11.25) |
(11.26) |
The basic chirplet can be regarded as an exponential polynomial signal in which the polynomial is of order 2. Exponential polynomials of higher order have also been explored [89,90,91]. (See also §G.8.2.)