The CWT tiling of the plane is useful because many real-world signals have slowly oscillating content that occurs on long scales, while high frequency events tend to be abrupt or transient. The instantaneous frequencies are resolved early in the signal, but not as well later. The helper function plots the instantaneous frequencies over the spectrogram as black dashed-line segments. The source code for helperPlotSpectrogram is listed in the appendix. Use the helper function helperPlotSpectrogram to plot the spectrogram of the signal with a time window size of 200 milliseconds. The instantaneous frequencies of the two chirps at their initial time points are approximately 5 Hz and 15 Hz.
If you can estimate the frequency components you are expecting in your signal, then you can use that information to pick a window size for the analysis. Once you pick a window size, it remains fixed for the entire analysis. Conversely, choosing a larger window helps obtain good frequency resolution at the expense of time resolution. For time-frequency analysis using the STFT, choosing a shorter window size helps obtain good time resolution at the expense of frequency resolution. However, choosing a window (segment) size is key. The STFT provides some information on both the timing and the frequencies at which a signal event occurs.
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