Simple TFR
Main TFR Page | Synthetic Signal Page
Here is a quick and easy TFR -- it is simply using the spectrogram as a mask for the scalogram. This distribution is entirely positive, and does not suffer from the cross-term interference of the WVD or other quadratic forms. This representation compares well to the other quadratic distributions such as the RID, Choi-Williams Distribution, ZAM, etc., and I present some plots with the gridlines spaced to show the time/frequency behavior of the signal.
The wavelet method brings excellent temporal resolution across nearly the entire frequency range, and the spectrogram method gives good temporal and frequency resolution. Combining them provides an easy way to visually compare the results of other TFR methods. This simple TFR has a few significant drawbacks, most obviously is the attenuation of higher frequency components. The scale -> frequency transformation is an approximation, as the frequency content of a wavelet is somewhat diffuse, and "leaks" across frequency ranges. Thus, the amplitudes of the two transient signals in the wavelet plot are different, while the area under the curve (energy integral) is approximately the same. (The higher frequency component is broader along the frequency axis, with a smaller peak; the lower frequency component is narrower along the frequency axis, with a higher peak.) When this is overlain with the spectrogram, the high-frequency transient signal is decreased relative to the medium-frequency transient -- we would expect their amplitudes to be roughly the same given the character of the signal (c.f. the spectrogram plots below, and the other TFR methods described on the main TFR page and the synthetic signal page).
Plots below show the Spectrogram, Scalogram, and Simple TFR plots. Spectrogram examples are calculated using two different window lengths (N/4 and N/8), to again demonstrate the Time-Frequency resolution tradeoff inherent to the Spectrogram method.
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