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).

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.

Knowledge and understanding:

At the end of the course, the student will learn the fundaments of signal and image analysis; will know how signals and images can be processed using digital filters; will know the main digital filter structures and how these can be designed; will learn the basic principles of audio, image, and video compression; moreover, he will acquire the ability to understand the principles and methods at the basis of any digital signal processing system.

Applying knowledge and understanding:

The student will learn the methodologies of digital signal processing (DSP) and will be able to apply them for processing audio signals, images, videos, and more in general any mono- or multi-dimensional signal. In particular, he will be able to analyze signals, to process them using digital filters, to design different kinds of DSP filters, to understand and apply the main signal compression methods. The ability to apply these techniques will be developed and sharpened in the laboratory exercitations, where audio signals, images, and video signals will be analyzed, processed, or compressed, and where different DSP systems will be designed.

Making judgements:

The student will be able to apply the methodologies of digital signal processing for understanding and solving novel problems involving signal analysis, signal processing, or signal compression. The critical discussions in class and the exercitations will be used to stimulate and develop the making judgements ability of the student.

Communication skills:

The student will acquire the ability to communicate the fundamental concepts of digital signal processing with an appropriate and rigorous terminology. He will learn to describe the problems related to signal analysis, signal processing, and signal compression and the methodologies adopted for their solution.

Learning skills:

The student will acquire the ability to study and learn novel techniques for signal analysis, signal processing, and signal compression, and he will be able to develop autonomously solutions for novel problems related to digital signal processing.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

On the Blendead Learning website are published: i) the lecture notes of the signal processing part; ii) the slides of the image processing part; iii) the indication of all books chapters used for preparing the lessons.

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.
 

Assessment

Written exam and oral exam.

The written exam is composed by a design exercise and two open answer questions: the first related to the signal processing part of the course, the second to the image processing part. The written exam is evaluated in thirtieths and it is passed if the mark, which holds only for that scheduled exam, is at least 18/30. During the written exam, books and lecture notes cannot be used. The evaluation of the exercise (which assigns 10 points) is mainly related to the correctness of the design procedure. The evaluation of the open answer questions (which assign 10 points each) consider both the acquired knowledge and the ability to rigorously describe the topic.

The oral exam, which is composed by open answer questions,  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. The evalution of the oral exam consider the acquired knowledge, the comprehension of the subject, and the ability to properly present the topic.

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 offers additional e-learning facilities on the Moodle platform > elearning.uniurb.it