Mathematicians theorized its use in the early 1900's. Additionally, computations are directly proportional to the length of the input signal. In wavelet analysis, the scale that one uses in looking at data plays a special role. Wavelet algorithms process data at different scales or resolutions. This approach is known as multi-resolution analysis.
Wavelets are well-suited for approximating data with sharp discontinuities.
If one further chooses the best wavelets adapted to the data, or truncates the coefficients below some given threshold, the data is sparsely represented. For instance, the FBI uses wavelet coding to store fingerprints. Hence, the concept of wavelets is to look at a signal at various scales and analyze it with various resolutions. The freedom of the analyzing wavelet is a major difference between the two types of analyses and is important in determining the results of the analysis. A successful application presupposes some expertise on the part of the user.