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Definition of "harmonic analysis" |
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms. / the branch of mathematics dealing with the decomposition of signal functions as a linear combination of basis functions which represent “waves” of various frequencies. When the basis functions are sines and cosines each with a frequency that is an integer multiple of the signal’s frequency, we have trigonometric harmonic analysis, in other words classical Fourier analysis, which provides the amplitudes and phases of the constituent sinusoids. (See Fourier transform.) With other basis functions, for example wavelets, we have non-trigonometric harmonic analysis ( See wavelet, wavelet transform). Abstract harmonic analysis studies the generalization of Fourier analysis to abstract spaces. |
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