Analysing bird songs with Wigner transform

This makes sense because a periodic signal at time T would locally correlate with a time inverted version of itself, however in WDF this correlation isn't time bounded, so if the signal is 1 hour long, WDF will multiply two one hour long signals to compute just one value at T. This seems meaningless at first glance, as the random contributions 30 mins away from the current moment would make WDF random, but a closer look reveals that if those far away contributions are indeed random, they would cancel out each other, and they do. So it doesn't really add any complexity on top of the regular FFT. In practice WDF is an extremely noisy function that's much less insightful than plain FFT. Below is the same bird recording visualized with different methods. WDF is able to produce interesting spectrograms sometimes, but in most cases it's unusably noisy. Unlike FFT spectrograms, WDF gets more precise on larger windows: frequency lines get thinner, at the expense of adding more noise around them. Below is the same violin sample: an FFT spectrogram, and two WDF spectrograms with 2048 and 4096 samples per frame. Some bird examples: WDFs with 2048, 4096 and 8192 samples per frame. For some reason WDF is miles ahead on simple tibetian bowl sounds.