Discrete-time signals, sampling of analog signals, discrete-time Fourier transform. Z transform. Linear time-invariant (LTI) systems. Realization structures for LTI systems. Discrete Fourier transform (DFT), fast Fourier transform (FFT). Finite and infinite impulse response (FIR and IIR) filter design. Discrete-time random processes. Applications of digital signal processing systems.
Argenti F., Mucchi L., Del Re E., Elaborazione numerica dei segnali: Teoria, esercizi ed esempi al calcolatore, McGraw-Hill, 2011.
Other reference books:
 A. V. Oppenheim, R. W. Schafer, Discrete-time signal processing, 3a edizione, Prentice Hall, 2009.
 J. G. Proakis, D. G. Manolakis, Digital signal processing, 4a edizione, Prentice Hall, 2006.
 S. K. Mitra, Digital signal processing, 3a edizione, McGraw-Hill, 2005.
 T. W. Parks, C. S. Burrus, Digital Filter Design, Wiley, 1987.
 A. Antoniou, Digital filters: analysis, design and applications, 2a edizione, McGraw-Hill, 2000.
 C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Shafer, H. W. Schuessler, Computer-based exercises for signal processing using MATLAB, Prentice-Hall, 1994.
 V. K. Ingle, J. G. Proakis, Digital signal processing using MATLAB}, Brooks/Cole, 2000.
 Prati C., Segnali e sistemi per le telecomunicazioni 2/ed, McGraw-Hill, 2010.
 Gherardelli M., Fossi M. Appunti di teoria dei segnali: Segnali deterministici, Segnali aleatori, Società Editrice Esculapio, 2015.
The aim of the course is to provide the tools and basic methods for the representation, analysis and processing of time-discrete (TD) signals, deterministic and random.
Knowledge and understanding:
- knowledge of sampling of analog signals and methods for their reconstruction from TD signals;
- knowledge of the main mathematical transforms (Fourier transform, Z transform) to characterize the TD signals in the frequency domain;
- acquisition of the concept of filtering as processing of TD signals and the main methods for designing and implementing signal processing systems;
- ability to understand the theoretical and practical bases of the main applications of digital signal processing systems.
Ability to apply knowledge and understanding:
- ability to implement TD signal analysis algorithms for extracting information of interest;
- ability to design and implement TD signal processing systems via software
Limits, series, integrals. Trigonometry. Complex numbers. Linear algebra. Probability theory. Random variables. Fourier representation of analog signals, both periodic and aperiodic.
Type of Assessment
Written and oral exams. The written exam may be substituted by a computer project (maximum two students per project).
The aim of the first test (written or computer project) is to verify the ability to:
- knowing how to model a problem of acquisition and analysis of numerical signals, using both time and frequency domain;
- knowing how to extract information of interest from discrete-time signals;
- knowing how to design discrete-time signal processing systems based on known specifications or objectives.
The aim of the oral test is to verify:
- theoretical knowledge at the base of the sampling of analogue signals;
- theoretical knowledge and ability to use the main mathematical tools (Fourier transform, Z transform) for the frequency representation of signals and discrete-time systems;
- the ability to design, implement and use discrete-time signal processing systems.
Sampling of analog signals
Sampling theorem. Reconstruction of analog signals from sequences of samples. Sampling of bandpass signals. Sampling in non-ideal conditions. Quantization of sampled signals. Discrete-time Fourier transform (definition, convergence, properties, theorems). Discrete-time random processes.
Definition and convergence of Z transform. Inverse Z transform. Properties and theorems on the Z transform.
Discrete-time systems, linear time-invariant systems
Definition of discrete-time system. Linear time-invariant (LTI) systems, impulse response. Properties of LTI systems, serial and parallel connections, stability, causality. Examples of elementary LTI systems. Finite-difference linear equations. Transfer function. Frequency response. Phase and group delay, linear-phase LTI systems. Allpass systems and minimum-phase systems. Examples of significant time-varying linear systems.
Structures for discrete-time systems realizations
Elementary components for the realization of LTI systems. Direct and transpose structures. Structures for linear phase FIR systems. Cascade and parallel realizations.
Discrete Fourier Transform
Representation of discrete-time periodic signals by means of discrete Fourier transform (DFT). Relationships between DFT, Z transform and Fourier transform. Properties of DFT. Circular convolution. Fast algorithms for DFT computation: FFT with time and frequency decimation. Fast convolution. Spectral analysis.
Design Methods for FIR Filters
Design specifications. Properties induced by the symmetry of the impulse response. Window method and examples of bandpass, derivative and Hilbert filter design. Least squares method. Frequency sampling method. Equiripple method.
Design Methods for IIR Filters
Indirect design methods. Design of analog prototypes (Butterworth, Chebyshev, elliptical filters). Direct design methods.
Examples of applications of signal processing systems.