The fourier, fouriersin,and fouriercos transforms are exceptionally interesting and useful examples of integral transforms. The fourier transform itself has many beautiful properties that make it useful in engineering sciences. The fouriersin and fouriercos transforms have uses in spectral analysis of real sequences, in solving some boundary value problems, and in transforming domain processing of digital signals. The inverse fourier transform is simply a front end for fourier.
The definitions of the transforms:
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| (1.1) |
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| (1.2) |
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| (1.3) |
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| (1.4) |