Wavelet function originates from multiresolution analysis, and its basic idea is to express the spread function f(t) as a series of successive approximation expressions, each of which is a smooth form of f(t) motion, and they correspond to different resolutions respectively. Multi-resolution analysis, also known as multi-scale analysis, is a theory based on the concept of function space, and its idea comes from engineering. Founder Mallat. S established this theory when studying the problem of image processing.

At that time, a very common method for people to study images was to decompose images at different scales and compare the results to obtain useful information. Meyer's orthogonal wavelet basis makes Mallat think about whether to use the multi-scale characteristics of orthogonal wavelet basis to expand the image in order to obtain the "information increment" between different scales of the image.

This idea led to the establishment of multi-resolution analysis theory. MRA not only provides a simple method for the construction of orthogonal wavelet bases, but also provides a theoretical basis for the fast algorithm of orthogonal wavelet transform. Its idea coincides with multi-sampling rate filter banks, which enables us to combine wavelet transform with mathematical filter theory. Therefore, multi-resolution analysis plays a very important role in orthogonal wavelet transform theory.