Portale di Ateneo - En.Unibs.it

Introduction
Course motivation and covered topics.

Digital Sequences and Systems
Elementary sequences. Sequence classification. Sequence generation. Elementary operations.
Discrete systems. Linearity. Stability. Causality. Translation Invariance. Characterization of Linear Translation Invariant (LTI) system in the time domain: FIR and IIR families, AR, MA and ARMA families. Linear difference equations. Sequence convolutions and correlations (linear, normalized, circular).

Frequency analysis of a digital LTI system
Time Fourier Transform (DTFT): Definition and properties. Convergence issues. Gibbs fenomenons. Frequency analysis of a digital LTI system.

A-D and D-A conversion
Ideal and real sampling. Aliasing. Sufficient conditions for no aliasing. Ideal interpolation. ZOH interpolation. Digital implementation of an Analog System. Analog implementation of a Digital System.

Z Transform
Definition and properties. Regions of Convergence. Poles and Zeros. Z transform properties for causal, non causal and anti-causal sequences. Inverse Z transform. Relationships between Z transform and DTFT.

ARMA system classification
Comb filters. Minimum phase filters. Linear phase filters. All-pass filters.

Discrete Fourier Transform (DFT)
Definition and properties. Relationships with DTFT and Z transform. Sampling in frequency. Circular time axis. Introduction to FFT. Indirect implementation of the linear and circular convolutions. Long sequence filtering: Overlap-Add and Overlap-Save techniques.
Deterministic sequence spectral estimation. Windows families.

Introduction to FIR and IIR filter design
FIR Filters. Sampling in frequency approach. Windowing of ideal filter impulse response. Parks-Mc Clellan technique.
IIR Filters. Butterworth filters. Impulse invariance. Bilinear transformation.

Non parametric spectral estimation
Sampling of a stochastic process. Non parametric spectral estimation. The periodogram. Bartlett, Welch, Blackman-Tukey methods.

Implementation of discrete time systems
Basic structures for the implementation of FIR and IIR systems. Frequency sampling. Effects of the quantization.

Multirate signal processing
Decimation and interpolation of sequences. Poliphase implementation of FIR filters.

Conclusions
Concluding remarks and examples of practical applications.