Signal Processing
A.Y. 2024/2025
Learning objectives
The course has the goal of providing the basic theoretical knowledge of (i) the theory of continuous-time signals and (ii) of discrete-time digital signal processing by means of linear time-invariant systems.
Expected learning outcomes
The student will acquire the theoretical skills necessary to sample a continuous-time signal; also she/he will be able to represent a discrete-time signal in the frequency domain; finally, the student will be able to analyze and design a linear time-invariant filter to process discrete-time signals.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
· Introduction. Continuous-time and discrete-time signals. Systems. Review of complex numbers. Phasors.
· Time-continuous sinusoidal signals. Frequency. Harmonic frequencies and periodical signals.
· Digital signals: sampling and quantization. Sampling of continuous-time signals and the sampling theorem. Aliasing. Reconstruction of continuous-time signals from samples and interpolation.
· Analysis of discrete-time signals in the frequency domain. Discrete-time Fourier Transform (DTFT), Discrete Fourier Transform (DFT) and FFT algorithm. Spectral characterization of sampled signals.
· Linear time-invariant systems (LTI). Impulse response. Stability and causality. Systems interconnection (series, parallel, feedback). Finite-difference equations as representation of LTI systems.
· Zeta transform. Definition and principal properties. Region of convergence. Analysis of LTI systems via Zeta transform. Transfer functions, poles and zeros. Frequency response. Stability condition in the Zeta domain
· FIR filters. Linear phase and LTI filter with symmetrical impulse response. FIR filters design with the window method.
· IIR filters. Design by poles and zeros placement. Design of digital IIR filters starting from their analog counterparts.
Warning: the class is taught in Italian. The course syllabus is provided here for reference only.
· Time-continuous sinusoidal signals. Frequency. Harmonic frequencies and periodical signals.
· Digital signals: sampling and quantization. Sampling of continuous-time signals and the sampling theorem. Aliasing. Reconstruction of continuous-time signals from samples and interpolation.
· Analysis of discrete-time signals in the frequency domain. Discrete-time Fourier Transform (DTFT), Discrete Fourier Transform (DFT) and FFT algorithm. Spectral characterization of sampled signals.
· Linear time-invariant systems (LTI). Impulse response. Stability and causality. Systems interconnection (series, parallel, feedback). Finite-difference equations as representation of LTI systems.
· Zeta transform. Definition and principal properties. Region of convergence. Analysis of LTI systems via Zeta transform. Transfer functions, poles and zeros. Frequency response. Stability condition in the Zeta domain
· FIR filters. Linear phase and LTI filter with symmetrical impulse response. FIR filters design with the window method.
· IIR filters. Design by poles and zeros placement. Design of digital IIR filters starting from their analog counterparts.
Warning: the class is taught in Italian. The course syllabus is provided here for reference only.
Prerequisites for admission
The courses "Continuum mathematics" and "Mathematical methods for digital communication" are preparatory for the course "Signal Processing".
Teaching methods
The course will be composed of: a) academic lectures; b) solution of exercises, also previously assigned to the students; c) hands-on learning by exemplification of some of the topics covered during the course by using a professional software for digital signal processing (Matlab).
Teaching Resources
After each class, the copy of what written on the electronic board will be made available on the Ariel course web site: https://myariel.unimi.it/course/view.php?id=2316
The reference textbook is:
James H. McClellan, Ronald W. Schafer, Mark A. Yoder
Digital Signal Processing First, Second edition (o DSP First, 2nd edition)
Pearson Education, 2016. ISBN-13: 978-1292113869
Notes of some of the classes of the previous academic year, as prepared by past students, are also available.
The reference textbook is:
James H. McClellan, Ronald W. Schafer, Mark A. Yoder
Digital Signal Processing First, Second edition (o DSP First, 2nd edition)
Pearson Education, 2016. ISBN-13: 978-1292113869
Notes of some of the classes of the previous academic year, as prepared by past students, are also available.
Assessment methods and Criteria
The exam is composed by a written examination (90% of the final grade), followed by an oral examination (10% of the final grade).
The written examination requires:
- to solve practical exercises (similar in complexity and formulation to those assigned to the students during the course and solved together).
- to answer open-ended questions related to knowledge provided during the course.
The written examination lasts 2 hours and the use of textbooks or personal notes is not permitted.
The oral examination is composed by a discussion of the written examination and by brief questions.
The final grade is assigned on a scale of 30, considering the following criteria: knowledge of the topics, ability in applying the knowledge acquired on practical problems, clarity in expressing concepts.
The written examination requires:
- to solve practical exercises (similar in complexity and formulation to those assigned to the students during the course and solved together).
- to answer open-ended questions related to knowledge provided during the course.
The written examination lasts 2 hours and the use of textbooks or personal notes is not permitted.
The oral examination is composed by a discussion of the written examination and by brief questions.
The final grade is assigned on a scale of 30, considering the following criteria: knowledge of the topics, ability in applying the knowledge acquired on practical problems, clarity in expressing concepts.
INF/01 - INFORMATICS - University credits: 6
Practicals: 12 hours
Laboratories: 16 hours
Lessons: 32 hours
Laboratories: 16 hours
Lessons: 32 hours
Professor:
Sassi Roberto
Shifts:
Turno
Professor:
Sassi RobertoProfessor(s)
Reception:
By appointment (email or phone)
Dipartimento di Informatica, via Celoria 18, stanza 6004 (6 piano, ala Ovest), Milano or remotely via Microsoft Teams