ABSTRACT
Fourier analysis is provided with different tools, which are appropriate for particular type of signals. If the signal is periodic and deterministic, Fourier series analysis is used. If the signal is finite and deterministic, the Fourier transform (FT) is used. With the development of an efficient computational procedure, known as the fast Fourier transform (FFT), the discrete FT (DFT) is used extensively. As a practical matter are only able to manipulate a certain length of a discretized continuous signal. Because the DFT uses finite number of samples, one must be concerned about the effect that the truncation has on the Fourier spectrum, even if the original function extends to infinity. The reader should also find the spectrums of the windows and get familiar with level of their side-lobes and, in particular, the level of the first side-lobe. The convolution property of the linear time-invariant functions and the FT property of the convolution of two functions obtain the frequency spectrum.
