If we take only a part of the wavelet spectra (see denoising), we can use it to construct the approximation of the original signal. As the wavelet trasform is a best decomposition transformation for the non-stationary signals, it should be good also to compress them by this way. Here a samples of such a compression and decompression for a "Vari baba trnku" signal (see continuous wavelet transform for the signal details). Signal was compressed and than decompressed using this method. The signal is presented here after this treatement as a *.wav file to prevent any other changes that could happen while using MP3 or some other format.
From the next samples it is clear that the mentioned compression procedure is not as good for a given signal as it was supposed to. At the 38 percent compression (the compression treshold obtained by denoising alogithm) there is no signal corruption seen. Fof higher cmpressions, there is a more or less significant corruption, and for the two highest compressions (1 and 2 percent) the decompressed signal is allready very bad.
I suppose that the main problem here is the high sampling frequency of the signal (44.1 kHz). As we have the sampling frequency much higher than the highest frequencies in the spectrum, the signal is not that "non-stationary" as it could be. The frequencies are changing extremely slowly in the signal, and therefore some other compression (for example the MP3 one with windowed FFT) will probably win for such a signal. If we have signal with lower sampling rate, I would expect better results.
In the other side, the proper choose of the wavelet, the wavelet spectra tresholding etc. could improve the compression even for this kind of signal. Note, that the algorithm used here was the simplest one possible, and the compression of the 262144 data took only 7 seconds (on Pentium III 500 Mhz processor). The same time took the decompression.
Created by Petr Klapetek, February 2002