Review of the sampling theorem from different points of view, both from the perspective of time and frequency. The continuous/discrete equivalent system. Practical implementation of sampling and quantification of signals. Introduction of multirate processing methods that allow the modification of the sampling period of discrete signals by decimating and interpolation.
The second part will deepen on the methods of frequency analysis of signals, with the development of the Discrete Fourier Transform (DFT) and its efficient version, the Fast Fourier Transform (FFT). The concept of windowing, resolution and dynamic range for the analysis of deterministic signals will be introduced. The concepts of random signals and their spectral estimation will be introduced, both in the case of stationary random (non-parametric) and non-stationary (STFT and spectrogram) signals.