DIGITAL SIGNAL PROCESSING
Learning outcomes of the course unit
1- Knowledge and understanding
Goal of the course is to provide the students with the basics of the analysis of discrete-time signals, the design of digital signal processing systems and digital filtering.
2- Applying knowledge and understanding
Students learn how to analyze and design simple linear systems (digital filters) being aware of the capabilities an practical limitations of digital signal processing techniques.
"Signal theory" (suggested)
Course contents summary
- Discrete-time signals and systems.
- Discrete-time Fourier transform (DTFT)
- The z-Transform.
- Sampling of continuous-time signals
- Representation of LTI systems
- Discrete Fourier Transform (DFT).
- Digital filter design
- Discrete-time signals and systems (4 hours)
Basic discrete-time signals: unit impulse, unit step, real and complex exponential, periodic sequences. Discrete-time systems: memoryless, linear, time-invariant, causal, stable. Linear and time-invariant (LTI) systems and impulse response. Discrete convolution and properties of LTI systems. Difference equations.
- Discrete-time Fourier transform (DTFT) (4 hours)
Representation of sequences in the frequency domain. Frequency response. Representation of sequences through the Fourier transform. Definition and properties of the DTFT.
- The z-Transform (6 hours)
Definition and properties. Region of convergence and relationship between the z-transform and a system's properties. Inverse z-Transform. Transfer function of a LTI system.
- Sampling of continuous-time signals (4 hours)
Periodic sampling and frequency domain representation of sampled signals. The sampling theorem. Reconstruction of a signal from its samples. Discrete-time processing of continuous-time signals. Impulse invariance.
- Analysis and representation of LTI systems (4 hours)
Frequency response of LTI systems. System function. Minimum-phase systems. Representation of linear constant coefficients difference equations. Direct form I and II.
- Discrete Fourier Transform (DFT) (8 hours)
Discrete Fourier series and its properties. Periodic convolution. Sampling of the DTFT. DFT: definition and properties. Circular convolution. Use of the DFT in the implementation of LTI systems. Algorithms for the computation of the DFT. FFT algorithms and their complexity.
- Digital filter design (6 hours)
Definitions of the specifications of a filter. Design of IIR digital filters. Design of FIR filters.
- A.V. Oppenheim, R. W. Schafer , “Discrete-Time Signal Processing”, 3rd Edition, Pearson (2010)
- M. Laddomada, M. Mondin, "Elaborazione numerica dei segnali", Pearson (2007)
- M. H. Hayes, "Digital Signal Processing" (Schaum's Outline Series) McGraw-Hill Education (1998 o 1999)
- D. G. Manolakis, V. K. Ingle, "Applied Digital Signal Processing: Theory and Practice", (1st edition), Cambridge University Press (2011)
Classroom lessons (75%) and exercise sessions (25%). The exercises are handed to the students one week in advance. The students have the opportunity to discuss their solution with the instructor.
Assessment methods and criteria
- The first session foresees two intermediate written exams, the first after half of the unit, the second at its end. A sufficient mark in the intermediate exams allows to take an optional oral exam. The unit final mark is computed as the average of the two written exams and, if taken, of the oral exam.
- The next sessions foresee a written and an oral exam. The unit final mark is computed as the average of the written and the oral exams.
- In either case, the exam final mark is computed as the weighted average of the first (2/3 of the mark) and the second unit (1/3 of the mark) marks.
Information to students and various documents are provided through the platform: