Learning objectives
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 and their use in digital systems and communications.
2- Applying knowledge and understanding
Students learn how to analyze and design simple linear systems (digital filters) and digital communication systems, being aware of the capabilities and practical limitations of digital signal processing techniques.
Prerequisites
Suggested: Probabilistic methods for engineering, Signals and systems, Communication Systems.
Course unit content
- 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
Full programme
- 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. 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.
Bibliography
- A.V. Oppenheim, R. W. Schafer , “Discrete-Time Signal Processing”, 3rd Edition, Pearson (2010)
- M. Laddomada, M. Mondin, "Elaborazione numerica dei segnali", Pearson (2007)
- F. Argenti, L. Mucchi, E. Del Re, "Elaborazione numerica dei segnali", McGraw Hill (2011)
Teaching methods
Classroom lessons (about 75%) and exercise sessions (about 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
- For student following the course: intermediate test at half of the lectures period, second part on the day of the first exam.
- For everyone else: written exam.
Exams contain both exercises and theoretical questions. The instructor can decide to convert the written exam to an oral exam if the number of registered students is low.
Other information
Information to students and various documents are provided through the platform elly
