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 Definition: A wavelet is a mathematical function used to divide a given function or continuous-time signal into different frequency components and study each component with a resolution that matches its scale.
A wavelet transform is the representation of a function by wavelets.
The wavelets are scaled and translated copies (known as 'daughter wavelets') of a finite-length or fast-decaying oscillating waveform (known as the 'mother wavelet'). Wavelet transforms have advantages over traditional Fourier transforms for representing functions that have discontinuities and sharp peaks, and for accurately deconstructing and reconstructing finite, non-periodic and/or non-stationary signals.
In formal terms, this representation is a wavelet series representation of a square-integrable function with respect to either a complete, orthonormal set of basis functions, or an overcomplete set of Frame of a vector space (also known as a Riesz basis), for the Hilbert space of square integrable functions.
Wavelet transforms are classified into discrete wavelet transforms (DWTs) and continuous wavelet transforms (CWTs). Note that both DWT and CWT are of continuous-time (analog) transforms.
They can be used to represent continuous-time (analog) signals.
CWTs operate over every possible scale and translation whereas DWTs use a specific subset of scale and translation values or representation grid.
Source: Wikipedia (http://en.wikipedia.org/wiki/Wavelet)
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