The wavelet allows a rapidly changing time history (e.g. door slam noise) to be investigated in the frequency domain. The Fourier transform decomposes a signal using a set of sine waves as the basis functions. The Wavelet transform decomposes a signal using a set of wavelets, these are concentrated in time resulting in a higher time localization of the signal's energy. The basis wavelet function is scaled such that it is narrow at high frequencies and wide at low frequencies. In this way the wavelet can be considered as a series of constant relative bandwidth filters. This allows low frequencies to be analysed with a longer time axis than high frequencies, this is appropriate as low frequencies change more slowly with time than high frequency phenomena. The product between time (rms duration) and frequency (rms bandwidth) resolution cannot be smaller than 1/4pi according to Heisenberg Uncertainty Principle.
See also: Joint Time Frequency Analysis.