Abstract
Generally speaking, the method of signal analysis is built on the basis that signal decomposition is an orthogonal component. There are different selection ways for the sets of orthogonal functions after transformation and the transformation of orthogonal functions does not affect expressed functions themselves. Aiming at different requirements for application, different sets of orthogonal functions need to be used. This thesis not only studies classical and modern sets of orthogonal functions Fourier and wavelet sequence but also proposes prospects for the new application of the sets of orthogonal functions.
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