SIGNAL PROCESSING for MULTIMEDIA APPLICATION

Objectives

The course aims to provide students with the fundamental knowledge and methodological tools required for the analysis and digital processing of signals, with particular reference to multimedia applications and, specifically, to the processing of audio sequences. The principles underlying the digitisation of analog signals will be addressed, including issues related to sampling, quantisation, coding, and signal reconstruction, as well as the effects of phenomena such as aliasing, quantisation noise, and distortion.

In particular, the fundamentals of discrete-time signal and system analysis will be introduced through the study of the Discrete-Time Fourier Transform (DTFT), the Z-Transform, the Discrete Fourier Transform (DFT), and the related Fast Fourier Transform (FFT) algorithms. The characteristics of linear time-invariant systems, their representation in the time and frequency domains, and the main techniques for the design of FIR and IIR digital filters will also be explored in depth.

The course will also provide content on the use of MATLAB and related software tools for the analysis, simulation, and design of digital signal processing systems, as well as for the spectral analysis and filtering of signals and audio sequences.

The course includes practical sessions aimed at providing students with hands-on skills in the use of software tools for the generation, analysis, and processing of digital signals. These activities, including the design and experimental validation of digital filters and the processing of audio sequences, represent an important opportunity to develop practical skills, the ability to analyse results, and problem-solving skills.

Students will also be able to collaborate with their peers in group activities and to critically discuss design solutions and the results obtained, thereby developing transferable skills useful in technical, scientific, and professional activities.

Knowledge and understanding

Based on the knowledge acquired during the course, students will be able to understand techniques for the digitisation, transformation, and processing of signals; coding, compression, and multimedia transmission techniques; the properties of discrete-time systems; and techniques for the analysis and design of digital filters for multimedia applications.

Applying knowledge and understanding

By the end of the course, students will be able to analyse discrete-time signals and systems, use time-domain and frequency-domain analysis tools, and design FIR and IIR filters, evaluating their performance using MATLAB and applying them to real-world signals.

Making judgements

By the end of the course, students will be able to evaluate and interpret experimental laboratory data, critically analyse the characteristics and performance of digital signal processing systems, and select the most appropriate analysis, processing, and filtering techniques according to the specific application requirements. These skills will also be developed through guided exercises and practical activities.

Communication skills

By the end of the course, students will be able to discuss topics related to digital signal processing using appropriate technical terminology. They will also be able to analytically describe and document the methodologies adopted and the results of the analysis, simulation, and design activities carried out; prepare technical reports and design documentation; work effectively in teams; and present experimental results.

Learning skills

By the end of the course, students will have acquired the ability to independently explore topics related to digital signal processing and its multimedia applications. They will also be able to understand technical and scientific texts and to independently use new methodologies and software/hardware tools.

The course includes both face-to-face lectures (49 hours, corresponding to 7 ECTS credits) and laboratory sessions (30 hours, corresponding to 2 ECTS credits), aimed at putting the theoretical concepts into practice. Laboratory activities are carried out individually or in groups. The final course session is an outdoor class involving the use of drones to acquire data and images, which students will subsequently use in the preparation of a final course project.

The above teaching methods are consistent with the learning objectives of the course, which aim both to provide knowledge of tools for the analysis and synthesis of digital signals and discrete-time LTI systems and to apply these skills in experimental scenarios.

Should the course be delivered in blended or distance-learning mode, the necessary changes may be introduced with respect to the arrangements described above, in order to ensure compliance with the programme set out in this syllabus.

Essential knowledge:

• Teorema del campionamento
• Variabile aleatoria Gaussiana
• Rappresentazione di un segnale nel dominio della frequenza
• Trasformata di Fourier
• Segnali notevoli (sin, cos, sinc, unit step)
• Laplace Transform
• Scala logaritmica e decibel

 Important knowledge:

• Definition of BIBO (Bounded-Input, Bounded-Output) stability
• Amplitude and phase distortions of an LTI system
• Low-pass, band-pass, and high-pass filters

 Useful knowledge:

• Representation of a discrete-time LTI system in the Z-plane, including poles and zeros
• Use of the MATLAB environment
• Butterworth, Chebyshev, and elliptic analog filters

Attendance is not compulsory.

However, attendance is strongly recommended, also in view of the highly experimental nature of the topics covered.

Detailed Programme

Part 1: Course Introduction (1 hour)

[Lectures: 1 hour – Practice and Labs: 0 hours]

• Course objectives
• Examination arrangements
• Teaching materials

Part 2: Signal Digitisation (3 hours)

[Lectures: 2 hours – Practice and Labs: 1 hour]

• A/D and D/A conversions
• Sampling and quantisation under non-ideal conditions
• Reconstruction of an analog signal from a digital sequence under non-ideal conditions

Part 3: Fourier Transform for Sequences and the Z-Transform (17 hours)

[Lectures: 8 hours – Practice and Labs: 9 hours]

• Canonical sequences
• Discrete-Time Fourier Transform (DTFT)
• Z-Transform for sequences

Part 4: Discrete-Time Systems (20 hours)

[Lectures: 13 hours – Practice and Labs: 7 hours]

• Linear time-invariant (LTI) systems, distortionless systems, all-pass systems, and minimum-phase systems
• Symmetric FIR filters
• Elementary canonical discrete-time systems

Part 5: Discrete Fourier Transform (DFT) (18 hours)

[Lectures: 12 hours – Practice and Labs: 6 hours]

• Definition and relationship with the DTFT and the Z-Transform
• Spectral estimation and Short-Time Fourier Transform (STFT)
• Real-time computation of the output of an FIR system

Part 6: Design and Implementation of Digital Filters (15 hours)

[Lectures: 11 hours – Practice and Labs: 4 hours]

• Design specifications and introduction to design techniques
• Main FIR filter design techniques
• Main IIR filter design techniques

Part 7: Processing of Aerial Images Acquired by Drones (5 hours)

[Lectures: 2 hours – Practice and Labs: 3 hours]

• Drone-based image acquisition using RGB, thermal, multispectral, and hyperspectral cameras
• 3D reconstruction through photogrammetry, LiDAR, and point clouds
• Use of artificial intelligence for the automatic construction of aerial image datasets and for image recognition
• Introduction to multispectral and hyperspectral image processing

Contribution of the Course to the Objectives of the 2030 Agenda for Sustainable Development

The topics covered in the course and the knowledge acquired contribute, directly or indirectly, to the development of sustainable technological solutions and to the provision of quality education, in accordance with Goals 3, 4, 7, 9, 11, 12, 13, 14, and 15 of the 2030 Agenda for Sustainable Development.

·        [2] A. V. Oppenheim and R. W. Schafer, “Discrete-Time Signal Processing, 3rd edition” Published by Pearson (August 18, 2009) © 2010.

·        [3] Lecture slides.

The examination consists of an oral examination typically comprising three questions. One question concerns signal digitisation, the Fourier Transform for sequences, and the Z-Transform; one concerns discrete-time digital systems; and one concerns the design of FIR and IIR filters. The three questions are selected at random using an examination simulator provided together with the teaching materials. As detailed in the examination simulator, some questions require demonstrations of the use and configuration of MATLAB scripts, which are also provided as part of the examination materials.

Students who pass the mid-term assessment will take a simplified oral examination consisting only of the second and third questions, while the first question will be considered passed.

Students who have also participated in the final course session, which consists of the acquisition of images and data using drones, may present a project agreed upon with the lecturer. This project will replace the second question and, in this case, the oral examination will consist only of the third question.

The oral examination will be assessed on the basis of the formal correctness and relevance of the topics discussed, the quality of the technical language used, and the ability to provide the correct solution to the problems presented.

Mid-Term Assessments

The mid-term assessment has a duration of three hours and consists of solving a number of laboratory exercises in the MATLAB environment. The outcome of the mid-term assessment will be one of the following: “Passed”, “Passed with reservations”, or “Not passed”. Students who receive a “Passed with reservations” outcome may request, on a date to be agreed with the lecturer and before the beginning of the oral examination, the opportunity to address the topics for which critical issues have been identified. If these critical issues are successfully addressed, the outcome will be changed to “Passed” for the purpose of taking the oral examination.

The validity of each mid-term assessment is limited to the academic year in which the assessment is taken and will remain valid for six months from the end of the teaching activities of the relevant academic year.

Learning assessment may also be carried out on-line, should the conditions require it. To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l’integrazione Attiva e Partecipata — Servizi per le Disabilità e/o i DSA) referring teacher within their department (https://www.cinap.unict.it/content/referenti).

• Z-Transform: Definition; relationship with the Fourier Transform; conditions of convergence; region of convergence (ROC); ROC of finite sequences and of right-sided and two-sided sequences.
• Linear systems: Examples of discrete-time linear systems. Definitions of discrete-time systems, linear systems, and linear time-invariant (LTI) systems. For LTI systems: impulse response and computation of the output sequence (including a numerical example); linearity; causality; BIBO stability; examples of stable FIR and IIR filters.
• Representations of an LTI system: impulse response, finite-difference equation, transfer function, pole-zero representation, and frequency response. Conversion from one representation to another. Differences between FIR and IIR systems in the various representations.
• Symmetric FIR filters: properties, including linear phase, constant group delay, and zero locations; all-pass systems, including the properties of the numerator and denominator of the transfer function and the locations of poles and zeros; minimum-phase systems.
• Given a stable LTI system with one pole inside the unit circle and one pole outside the unit circle, determine its impulse response and discuss a possible implementation using a parallel or cascade connection of two stable systems.
• Given an LTI system described by a finite-difference equation, determine the transfer function and implement a reversal of the frequency response, graphically comparing the resulting frequency response with that of the original system.
• Notch or band-stop filters (all-zero filters and filters with poles and zeros), including verification of the frequency response in MATLAB. Comb filters (Types I and II, and filters obtained through the substitution of z with z^L), including verification of the frequency response in MATLAB. All-pass filters (FIR and IIR), including verification of the frequency response in MATLAB.
• FIR filter design: window method; optimal window design; design of band-pass FIR filters, FIR differentiators, and FIR Hilbert transformers; least-squares method; frequency-sampling method.
• Using the MATLAB tools provided during the course, design a band-pass filter with a passband between 2 kHz and 3 kHz using the window method, assuming a system with a sampling frequency of 8 kHz. Then filter a speech sequence recorded using Audacity.
• Using the filterDesigner tool, design a Butterworth-template IIR band-pass filter between 2 kHz and 3 kHz, assuming a system with a sampling frequency of 8 kHz. Then export it to MATLAB and use it to filter a speech sequence recorded using Audacity.