SIGNAL PROCESSING for MULTIMEDIA APPLICATION

Knowledge and understanding the most important elements regarding digital communications

Capturing and understanding the basic elements to manage Discrete-time signals and systems numerically, also using in the Fourier and Z domains.

Improving capabilities to analyze and design digital filters.

Applying knowledge and understanding of the state-of-art technologies of digital communications systems, also targeted to the practical application in non-usual contexts

Skills development for analysis of digital signals through spectral analysis techniques and for design of a time-invariant linear system by means of its Fourier response.

The target is to allow the student to use this knowledge also for future systems, although different from the ones studied in this course.

Making judgements of the main topics of this course

Outgrowth of a sufficient level of making judgements in discovering the main peculiarities of timeinvariant linear systems and of tools not only for the design of simple systems like the ones studied during the course, but also of more complex systems, like the ones needed to manage audio and video signals, which require further maturation of what studied during the course.

Communication skills finalized to heterogeneous interlocutors

Outgrowth of an effective and high-level communications skill for topics regarding generation of multimedia signals, and also their processing and playout.

Learning skills of the evolutions of the topics studied during the course, independently

Outgrowth of skills for autonomous training regarding scientific evolution of digital signal processing to deepen new techniques for filtering and managing new digital signals with reference to techniques applied in scenarios of the “Internet of Sound” (IoS).

The course is composed of a part of theory, and a part of practice and laboratory activities.

In-depth knowledge of signal theory, and in particular Fourier analysis, sampling of an analog signal, frequency response of a linear time invariant system. Characterization of an analog linear system.

Topics

ETU 1. Signal Digitalization

·         Sampling, quantization and encoding. Ideal interpolation of baseband signals. Sampling in non-ideal conditions: signals that are not band-limited and non-instantaneous sampling. Compensation and non-ideal interpolation.

ETU 2. Fourier Transform of sequences, and Z-Transform

·         Definition of Fourier Transform of sequences. Inverse Fourier Transform of sequences. Fourier Transform of canonical sequences

·         Z-transform of sequences. Relationship with the Fourier Transform. Region of Convergence. Z-Transform of canonical sequences. Inverse Z-Transform of rational functions.

·         Convergence of Fourier and Z-Transforms. Inverse Z-Transform of non-rational functions

ETU 3. Discrete-Time Systems

·         Linear Time-Invariant (LTI) systems. Derivation of the output sequence; causality; stability. Representation of LTI systems by means of the impulse response; linear difference equation; transfer function; frequency response. Phase delay and group delay. Non-distortion systems. All-pass systems. Minimum-phase systems.

·         Symetric FIR filters: properties (linear phase, constant phase delay, position of the zeros)

·         Canonical discrete-time systems: time shifter, moving average, accumulator or digital integrator, digital differentiator, filter for downsampling, interpolator or umsampler, sequence multiplexer, half-band FIR, analytical signal generator.

ETU 4. Discrete Fourier Transform (DFT) e Fast Fourier Transform (FFT)

·         DFT e IDFT. Circular time shifting. Circular and linear convolutions. DFT and FFT application to derive the output sequence of a LTI system.

·         Decimation-in-time (DIT) radix-2 FFT

·         Spectral analyis, spectral resolution. Periodogram.

·         Fast linear convolution and application to sequence filtering. “Overlap & Add” e “Overlap & Save” algorithms.

·         Decimation-in-frequency (DIF) radix-2 FFT. Inverse FFT.

·         Window type and duration choice.

ETU 5. Design and Implementation of digital filters

·         FIR filters: design specifications. Application of linear-phase FIR filters. Windowed Fourier series. Low-pass filter design. Equiripple method and Chebichev criterium. Parks-McClellan approach.

·         IIR filters. Direct and indirect design methods. Bilinear transform and impulse-invariance method.

·         Optimal window design. Pass-band FIR filters. Differentiator FIR. Hilbert FIR. Least-squares design method. Frequency sampling design method. Minimum-phase FIR design.

·         Design of high-pass, band-pass and band-stop filters.

ETU 6. Processing and compression of audio and video sequences

·         Lossless and lossy encoding. A brief overview of encoding techniques of voice signals and JPEG and MPEG image encoding techniques

·         Creation of effects on digital images in Matlab

[Smi] The Scientist and Engineer’s Guide to Digital Signal Processing, Second Edition, Steven W. Smith, California Technical Publishing, San Diego, California.

[Opp] Alan V. Oppenheim, Ronald W. Schafer, Digital Signal Processing, Prentice Hall Digital Processing Series

[Pro] J. G. Proakis, D. G. Manolakis, Digital signal processing.

•        Analog-to-digital conversion: sampling, quantization and encoding; Guard band; ideal sampling, spectrum of the sampled signal, sampling theorem, aliasing and folding of the spectrum; quantization noise and SNR calculation; SNR for sinusoidal signal and for Gaussian signal; non-uniform quantization.

•         Definitions: Discrete-Time Fourier Transform (DTFT) for sequences, normalized frequencies, DTFT periodicity, inverse DTFT; canonical sequences and their DTFT

•         In Matlab: Sampling and reconstruction of an analog signal; graph of the original analogue signal, graph of the sequence obtained by sampling, graph of the DTFT of the obtained sequence

•         Representations of an LTI system: impulse response, finite difference equation, transfer function, poles / zeros representation; frequency response. Moving from one representation to another one. Differences between FIR and IIR on the different representations.

•         Given an LTI system described by a finite difference equation, discuss its possible stable and causal implementation, and calculate the output at given input sequences. Display the position of poles and zeros on the complex plane.

•         Notch and band-stop filters, comb filters and all-pass filters, with Matlab verification of the frequency response.

•         Spectral analysis, spectral resolution, choice of the window and its duration. Periodogram. Matlab laboratory - spectral estimates. Correlation between sequences.

•         Design in Matlab of a low-pass FIR filter with the window method