#### Simulation Results

Figure 10.24 shows the waveform of a Gaussian-windowed chirp (``chirplet'') generated by the following matlab code:

fs = 8000; x = chirp([0:1/fs:0.1],1000,1,2000); M = length(x); n=(-(M-1)/2:(M-1)/2)'; w = exp(-n.*n./(2*sigma.*sigma)); xw = w(:) .* x(:);

Figure 10.25 shows the same chirplet in a time-frequency plot.
Figure 10.26 shows the spectrum of the example chirplet. Note
the *parabolic fits* to *dB magnitude* and *unwrapped
phase*. We see that phase modeling is most accurate where magnitude
is substantial. If the signal were not truncated in the time domain,
the parabolic fits would be perfect. Figure 10.27 shows the
spectrum of a Gaussian-windowed chirp in which frequency
*decreases* from 1 kHz to 500 Hz. Note how the curvature of the
phase at the peak has changed sign.

**Next Section:**

Tightening the IFFTs

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Chirplet Frequency-Rate Estimation