DIGITAL SIGNAL PROCESSING

-- Discrete-time signals and systems.
Basic signals and elementary transformations. Sampling of continuous-time signals: sampling theorem, Nyquist condition, aliasing and anti-aliasing filtering. Representation of discrete-time signals in the frequency domain: the Fourier Transform of a sequence and its properties. Discrete-time systems and their properties: linear, time invariant, memoryless, stable, causal systems. Linear time-invariant systems (LTI) and the discrete convolution. Difference equations. Analysis of LTI systems in the frequency domain: the discrete-time complex exponential, the frequency response.
-- The z-Transform.
Definition and properties. Inversion of the z-Transform. Theorems and properties of the z-Transform. Transfer function of a LTI system. Rational transfer functions. Finite impulse response (FIR) systems and infinite impulse response (IIR) systems. Stability of discrete systems.
-- The Discrete Fourier Transform (DFT).
Definition, properties and use of the DFT. Circular convolution and relationship with linear convolution. Relationship with the Fourier Transform. Efficient computation of the DFT: the Fast Fourier Transform (FFT).
-- Digital processing of analog signals.
Simulation of analog systems. Design of IIR digital filters. Design of FIR filters.