Forms of the Fourier TransformSpectrum Analysis
Spectrum analysis, which is defined as the transformation of a signal from a time-domain representation into a frequency-domain representation, has its roots in the early 19th century, when several mathematicians were working on it from a theoretical basis. But it took a practical man, an engineer with a good mathematical background, to develop the rationale upon which almost all our modern spectrum analysis techniques are based. That engineer was Jean Baptiste Fourier, and he was working for Napoleon during his invasion of Egypt on a problem of overheating cannons when he derived the famous Fourier Series for the solution of heat conduction. It may seem a far cry from overheating cannons to frequency analysis, but it turns out that the same equations apply to both cases. Fourier later generalized the Fourier series into the Fourier Integral Transform. The advent of digital signal analysis naturally led to the so-called Discrete Fourier Transform and the Fast Fourier Transform or FFT
Forms of the Fourier Transform
The Fourier Integral Transform
The Discrete Fourier Transform
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