The Course has the objective of introducing the basic concepts of signals and images, of presenting the fundamental principles and methods for signal analysis and signal processing using discrete time systems, and of illustrating the main techniques for compressing audio signals, images and video signals. 

01 Signals and signal processing:
 01.01 Characterization and classification of signals.
 01.02 Digital signal processing: pros and cons.

02 Discrete-time signals in the time domain.
 02.01 Time domain representation.
 02.02 Operations on sequences. 
 02.03 Classification of sequences.
 02.04 Basic sequences.

03 Discrete-time signals in the frequency domain:
 03.01 The Fourier series.
 03.02 The Continuous-Time Fourier transform (CTFT).
 03.03 The Discrete-Time Fourier Transform (DTFT).
 03.04 Properties of DTFT.
 03.05 The sampling theorem.

04 Discrete-time systems:
 04.01 Examples of simple systems.
 04.02 Classification of discrete-time systems. 
 04.03 Impulse response and convolution sum.
 04.04 Frequency response.

05 The Z-Transform:
 05.01 Definition of the Z-Transform. 
 05.02 The inverse Z-Transform. 
 05.03 Properties of the Z-Transform. 
 05.04 The Transfer Function. 

06 The Discrete Fourier Transform:
 06.01 Definition of the Discrete Fourier Transform (DFT).
 06.02 The relation between DFT, DTFT and Z Transform.
 06.03 Properties of the DFT.
 06.04 The Fast Fourier Transform (FFT).
 06.05 Linear convolution and circular convolution. 
 06.06 Frequency analysis with DTFT and DFT.
 06.07 The Discrete Cosine Transform (DCT).
 06.08 The Haar Transform.

07 Discrete-time LTI systems in the frequency domain:
 07.01 Ideal filters. 
 07.02 Phase delay and Group delay. 
 07.03 Zero-phase filters.
 07.04 Linear phase FIR filters.
 07.05 Geometric interpretation of frequency response computation.
 07.06 Simple digital filters.
 07.07 Comb filters.
 07.08 All-pass filters.
 07.09 Minimum-phase and maximum-phase transfer functions.
 07.10 Inverse system.
 07.11 Deconvolution. 
 07.12 Magnitude equalizer and phase equalizer. 
 07.13 Stability test for IIR filters (stability triangle, Schur-Cohn stability test).

08 Digital filter structures: 
 08.01 Basic building blocks. 
 08.02 FIR filter structures (direct form realization, cascade realization, frequency-sampling structure, lattice structure).
 08.03 IIR filter structures (direct form realization, transposition principle, cascade realization, parallel form realization, lattice ladder realization).

09 Finite precision arithmetic effects (Outline): 
 09.01 Finite precision arithmetic.
 09.02 Filter coefficients quantization. 
 09.03 A/D conversion noise.
 09.04 Uncorrelated noise due to rounding or truncation in multiplications.
 09.05 Overflow in additions.
 09.06 Limit cycles. 

10 Digital filter design: 
 10.01 Digital filter design specifications. 
 10.02 IIR filter design.
 10.03 FIR filter design.

11 Digital image processing fundamentals: 
 11.01 Introduction. 
 11.02 The human eye.
 11.03 Light and electromagnetic spectrum. 
 11.04 Image acquisition.
 11.05 An image formation model. 
 11.06 Digital image representation. 
 11.07 Spatial and gray-level resolution.
 11.08 Image interpolation.
 11.09 Spatial geometric transformations.

12 Intensity transformation and spatial filtering: 
 12.01 Basics.
 12.02 Gray level transformations (image negatives, logarithmic transformations, power-law (gamma) transformations, piecewise-linear transformations, gray level slicing).
 12.03 Histogram processing (histogram equalization, histogram matching algorithm).
 12.04 Spatial filtering. 
 12.05 Smoothing spatial filters (smoothing linear filter, nonlinear filters based on order-statistics).
 12.06 Sharpening spatial filters (sharpening with second derivatives: the Laplacian method, unsharp masking and highboost filtering, sharpening using first derivatives: gradient method).

13 Image filtering in the frequency domain: 
 13.01 2D Continuous Time Fourier Transform.
 13.02 2D sampling theorem. 
 13.03 Aliasing in images.
 13.04 2D Discrete Fourier Transform. 
 13.05 2D convolution theorem.
 13.06 Smoothing using frequency domain filters.
 13.07 Sharpening using frequency domain filters. 

14 Color image processing: 
 14.01 Color fundamentals.
 14.02 Color models (RGB model, CMY(K) model, HSI model).
 14.03 Pseudocolor image processing.
 14.04 Full-color image processing. 

15 Image compression: 
 15.01 Fundamentals.
 15.02 Some basic compression methods (Huffman coding, run-length coding, block transform coding, predictive coding).

16 Laboratory activities:
 16.01 Introduction to Matlab and Octave.

Although there are no mandatory prerequisites for this exam, students are strongly recommended to take it after Calculus, Discrete Structures and Linear Algebra, Probability and Statistics.

Teaching

Theory lectures and laboratory exercises, both face-to face and on-line.

Attendance

Although recommended, attendance course is not mandatory.

Course books

S. Mitra, "Digital signal processing", McGraw-Hill, 2001, 2011.
R. C. Gonzalez e R. E. Woods, “Elaborazione delle immagini digitali 3/Ed.”, Prentice Hall, 2008.
A. V. Hoppenheim e R. W. Schafer, "Discrete-time signal processing", Prentice Hall, 2010.
M. Laddomada e M. Mondin, “Elaborazione numerica dei segnali”, Prentice Hall, 2007.
Y. Q. Shi e H. Sun, “Image and Video Compression for Multimedia Engineering: Fundamentals, Algorithms, and Standards,” Second Edition, CRC Press, 2008.

Assessment

Written exam and oral exam.

The written exam is evaluated in thirtieths and it is is passed if the mark, which holds only for that scheduled exam, is at least 18/30. 

The oral exam can be performed only after passing the written exam and determines a spread between -5/30 and 5/30 of the previous mark, thus yielding the final mark. 

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

The course is offered both face-to-face and on-line within the Laurea Degree Program in Applied Computer Science.