Often one is interested in determining the frequency content of signals. Signals are typically represented as time dependent functions. Real signals are continuous or analog signals. However, through sampling the signal by gathering data, the signal does not contain high frequencies and is finite in length. The data is then discrete and the corresponding frequencies are discrete and bounded. Thus, in the process of gathering data, one seriously affects the frequency content of the signal. This is true for simple a superposition of signals with fixed frequencies. The situation becomes more complicated if the data has an overall non-constant trend or even exists in the presence of noise.
Fourier series, analysis, time series, signals, frequencies
