Knowledge and understanding: of the elementary principles and the most significant algorithms for processing one dimensional and multidimensional signals. Applying knowledge and understanding: providing the necessary knowledge to understand signal representation in the data and in the frequency domains, the FIR and IIR digital filters and their realization. Making judgments: to develop the ability to independently study, understand and critically evaluate the problems and their solutions in digital signal processing and in image processing. Communication skills: to develop the ability to communicate information, ideas, problems and solutions in the field of digital signal processing and image processing. Learning skills: to develop the necessary competence for studying novel algorithms for digital signal processing and image processing.

Prerequisites are the contents of all the courses deemed characterizing in the Bachelor degree, in particular about Signal theory. No specific propedeuticities within the Master degree.

- Discrete-time signals and systems in the time domain. - Discrete-time signals in the transform domain. - Discrete-time LTI systems in the frequency domain. - Digital filter structures. - Finite precision arithmetic effects. - Digital filter design. - Adaptive filters. - Multirate digital signal processing. - Digital image processing fundamentals. - Intensity transformation and spatial filtering. - Image filtering in the frequency domain. - Color image processing. - Image compression and coding.

S.K. Mitra, "Digital Signal Processing: A Computer-Based Approach", McGraw-Hill 2011 (4th ed.) R.C. Gonzalez, R.E. Woods, "Digital Image Processing", 4th Ed., Pearson 2018

- Discrete-time signals and systems in the time domain: operators; classification; fundamental sequences; sampling; linear, shift-invariant systems; causality and stability; convolution; interconnection of systems. - Discrete-time signals in the transform domain: the Discrete-Time Fourier Transform (DTFT); the Z-transform; the Discrete Fourier Transform; Linear convolution and circular convolution; Frequency analysis with DTFT and DFT; the short time Fourier Transform; the Discrete Cosine Transform (DCT). - Discrete-time LTI systems in the frequency domain: Ideal filters; phase delay and group delay; zero-phase filters; linear phase FIR filters; geometric interpretation of frequency response computation; simple digital filters; comb filters; all-pass filters; minimum-phase and maximum-phase transfer functions; inverse system; deconvolution; magnitude equalizer and phase equalizer; stability test for IIR filters (stability triangle, Schur-Cohn stability test). - Digital filter structures: basic building blocks; FIR filter structures (direct form realization, cascade realization, frequency-sampling structure, lattice structure); IIR filter structures (direct form realization, transposition principle, cascade realization, parallel form realization, lattice ladder realization); - Finite precision arithmetic effects: Finite precision arithmetic; filter coefficients quantization; A/D conversion noise; uncorrelated noise due to rounding or truncation in multiplications; overflow in additions; limit cycles. - Digital filter design: digital filter design specifications; IIR filter design: Butterworth, Chebyshev and elliptic filter; the bilinear transformation; direct methods for IIR filter design; FIR filter design. - Adaptive filters: Optimal Wiener filter, LMS, NLMS, RLS, APA algorithms, applications. - Multirate digital signal processing: basic sample rate alterations; multirate structures for sampling rate conversion; multistage design of decimator and interpolator; the polyphase decomposition. - Digital image processing fundamentals: the human eye; image acquisition; image formation model; digital image representation; spatial and gray-level resolution; image interpolation; spatial geometric transformations. - Intensity transformation and spatial filtering: gray level transformations (image negatives, logarithmic transformations, power-law (gamma) transformations); histogram processing (histogram equalization, histogram matching algorithm); spatial filtering; smoothing spatial filters (smoothing linear filter, nonlinear filters based on order-statistics); sharpening spatial filters (sharpening with second derivatives: the Laplacian method, unsharp masking and highboost filtering, sharpening using first derivatives: gradient method). - Image filtering in the frequency domain: 2D Continuous Time Fourier Transform; 2D sampling theorem; aliasing in images; 2D Discrete Fourier Transform; 2D convolution theorem; smoothing using frequency domain filters; sharpening using frequency domain filters. - Color image processing: color fundamentals; color models (RGB model, CMY(K) model, HSI model); pseudocolor image processing; full-color image processing. - Image compression and coding using the DCT and using wavelets; lossy and lossless coding.

Lessons about theory in classroom with slides; exercises on the blackboard, also using suitable computational tools; seminars. The teaching material, including exercises and problems, is made available to students through the Moodle and MS Teams platforms. Any arrangements for distance learning will be made in accordance with the guidelines laid down by the University.

The exam is oral and aims at verifying that the student is confident with the digital signal and image processing theory and algorithms, assessing his understanding of the subject and of signal processing practice. Two or three open questions and some exercises are asked during the exam, covering as far as possible the whole spectrum of the course contents. Final marks are the weighted average of the marks related to each question; weights can vary according to specific question. Examinees who answer all questions with full marks and demonstrate a brilliant critical knowledge of the course material will be awarded the laude.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)