This module covers the fundamental tools for digital signal processing. In particular it addresses topics of signal analysis and filtering concerning audio and image data both from the deterministic and the statistical viewpoint.

Participants will learn basic tools for digital signal filtering and analysis. In particular the program will be articulated in the following parts:

Fundamentals of digital signal processing

From Analog to Digital, from Continuous to Discrete:

Sampling and quantization, The Fourier Series (FS), the Fourier Transform (FT), the Fourier Discrete Time (DTFT) Fourier processing.

The z-Transform:

Its link to the DTFT and DFT, poles-zeros plots, ad-hoc filter design

Introduction to the DFT:

DFT, IDFT, derivation of the DFT, Fourier theorems for the DFT

Introduction to digital filters:

Time-domain representations, transfer function analysis, frequency response analysis

Windowing and STFT:

Overview of windows, overlap and add, STFT

Digital filter design techniques:

Filter specifications, IIR filter design, FIR filter design

Introduction to multirate processing:

Downsamplig, upsampling, decimation, interpolation, polyphase filters, perfect reconstruction filter banks.

Laboratory activities

Laboratory activities enable student to improve their understanding of the concepts learnt during the lectures. The proposed examples of applications and exercises, cover audio, image and video processing, and are based on Matlab^®