A main motivation for the development of various time-frequency distributions, such as the Short-Time Fourier Transform (STFT) spectrogram, the Wigner-Ville Distribution (WVD), the Gabor spectrogram, and so on, has been to describe how the energy of a signal varies with time and frequency.

Currently, scientists do not know of an algorithm, except for a few special cases, that can compute the energy of a signal at each particular time-frequency instant (t, f  ). Strictly speaking, the result of all quadratic time-frequency analysis algorithms, P(t, f  ), is nothing more than a certain type of weighted average energy in the vicinity of the point (t, f  ). Different weighting schemes lead to different algorithms with different time-frequency resolutions and other properties.

Without going into any detail, the following examples show the effect of different algorithms, or different weighting averages, and the resulting time-frequency distribution.

The following figure shows the STFT spectrogram of a test signal that contains ten sine cycles at 10 Hz. This example uses a Hanning window.

Although the signal starts at 1 s and ends at 2 s, the STFT spectrogram in the previous figure shows that energy exists before 1 s and after 2 s. You can use the Gabor spectrogram method with an order of four to suppress the energy substantially before 1 s, after 2 s, and above or below 10 Hz to achieve a better measurement, as shown in the following figure:

The previous figure shows that most of the energy of the signal now exists between 1 s and 2 s and within 10 Hz. As the order of the Gabor spectrogram increases, the energy concentration also increases, and you can come closer to achieving measurement between 1 s and 2 s and within 10 Hz. However, a Gabor spectrogram with a high order produces negative values, which can cause problems with the classical energy definition, which requires that the energy be non-negative.