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What is a wavelet?

What is a wavelet? Here are some definitions.

Noun
  1. A small wave; a ripple.
  2. (mathematics) A fast-decaying oscillation.
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Examples
The wavelet transform is designed to produce the best image possible given the bandwidth of the medium of transmission.
Introductory treaties on wavelet analysis with an emphasis on spline-wavelets and time-frequency analysis.
Spectral subtraction is useful for reducing hiss and two of the wavelet methods used are good at reducing crackle.
Development of model-based techniques for multibeam backscatter noise analysis and removal through wavelet techniques.
Most transient signals, which are exponentially damped sinusoids, cannot be wavelet basis functions because of their nonzero mean.
An excellent example of the working of the wavelet theory is found in the well-known pinhole camera.

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