Computational Data analysis of Fourıer Transformatıon by Numerical experiments(Numerical CODE)
The Fourier series (FS) and the Discrete Fourier Transform (DFT) should be thought of as playing similar roles for periodic signals in either continuous time (FS) or discrete time (DFT). Both analyze signals into amplitude, phases, and frequencies of complex exponentials; both synthesize signals by linearly combining complex exponentials with appropriate amplitude, phase, and frequency. Finally, both transforms have aspects that are extremely important to remember and other aspects that are important, but can be adjusted as necessary. As we work through some of the details, we’ll identify these very important and the not so important aspects. Frequency analysis is one of the key issues in the IEEE Society. Using computers in numerical calculations means moving into a non-physical, synthetic environment. Numerically, discrete or fast Fourier transformations (DFT or FFT) are used to obtain the frequency contents of a time signal and these are totally different than mathematical definition of the Fourier transform. This article simple reviews DFT and FFT with characteristic examples.
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