<mathematics> A waveform that is bounded in both frequency
and duration. Wavelet tranforms provide an alternative to
more traditional Fourier transforms used for analysing
waveforms, e.g. sound.
The Fourier transform converts a signal into a continuous
series of sine waves, each of which is of constant frequency
and amplitude and of infinite duration. In contrast, most
real-world signals (such as music or images) have a finite
duration and abrupt changes in frequency.
Wavelet transforms convert a signal into a series of wavelets.
In theory, signals processed by the wavelet transform can be
stored more efficiently than ones processed by Fourier
transform. Wavelets can also be constructed with rough edges,
to better approximate real-world signals.
For example, the United States Federal Bureau of Investigation
found that Fourier transforms proved inefficient for
approximating the whorls of fingerprints but a wavelet
transform resulted in crisper reconstructed images.
