Digital Signal Processing (ING-INF/01; CFU 6)
Prof. Giovanni Ramponi

Course programme

==== Introduction to digital signal processing

==== Discrete-time sequences
	data domain representations
	basic operations
	classification of sequences
	basic sequences
	the sampling process

==== Discrete-time signals
	definitions, examples
	linear and invariant systems
	causality and stability: definitions
	description in the time domain
	the convolution sum
	systems interconnection
	causality and stability: conditions
	classification of systems (FIR, IIR)
	auto- and cross-correlation of signals

==== Frequency domain representations
	the Discrete-Time Fourier Transform (DTFT): definitions and properties
	the Discrete Fourier Transform (DFT): definitions and properties
	linear and circular convolution
	convolution via overlap-add 
	Zeta transform: definitions and properties, ROC
	the Discrete Cosine transform (DCT): definitions and properties

==== Discrete-time systems in the transformed domain
	frequency response
	steady-state and transient response
	the concept of filtering
	phase and group delays
	the transfer function
	geometric interpretation of the frequency response
	poles positions and stability
	ideal filters
	zero-phase and linear-phase transfer functions
	types of linear-phase FIR filters
	simple FIR and IIR filters
	comb and allpass filters
	minimum- and maximum-phase systems
	inverse system; deconvolution
	sinusoidal oscillator

==== Filter design
	approximation theory
	design of IIR filters
	design of FIR filters

==== Digital filter structures
	block diagrams
	definition of canonic structure
	transposition rule
	direct, transposed, cascade, poliphase FIR filters
	linear-phase FIR filters
	ladder FIR filters (outline)
	direct I and II IIR filter forms
	cascade and parallel IIR filters
	lattice-ladder IIR filters (outline)
	first-order all-pass filters
 	complementary IIR filters (LP-HP, BP-BS)

==== Audio coding (basics)
	Description of the MP3 codec

==== Adaptive filters (basics)
	Description of the MP3 codec