Università Roma Tre

• Continuous and discrete signals and systems
Architecture of a communication system. Continuous and discrete signals: step and Dirac impulse signals, complex exponentials; elementary operations. Energy, power, periodicity of continuous and discrete signals; power of periodic signals. Linear, time-invariant, and causal systems. The impulse response. The Fourier series and its properties. Parseval theorem for periodic signals. The convolution and correlation of continue and discrete signals.

• Signals representation in the frequency domain
Fourier transform of continuous signals and its properties: linearity, time shift, frequency shift (modulation), product, duality, scale change, derivation, integration, convolution and correlation. Spectral energy density. Spectrum of periodic signals. Sampling theorem. Aliasing, energy and power of sampled signals. Reconstruction approaches of sampled signals. Fourier transform of discrete signals and its properties.

• Random signals
Basic concepts. Frequentist and axiomatic description. Continuous and discrete random variables. Cumulative distribution function, probability density (mass) function, characteristic function. Independent random variables. Joint, marginal and conditional probability density functions. Law of total probability. Bayes’ theorem. Gaussian, uniform, binomial, one-sides exponential statistics. Statistical moments of random variables: mean (expected value), variance, root mean square and their relations. Uncorrelated and statistically independent random variables. Functions of random variables and their probability density functions. Probability density function of the sum and the linear combination of independent random variables. Random processes and their statistics. Correlation and covariance. Stationary and ergodic processes. The harmonic process. The additive white Gaussian noise (AWGN). Random process through a system.

• Information theory and source coding
Basics of the information theory, self-information and entropy. Quantization. First Shannon theorem. Huffman coding.

• Baseband digital transmission
Binary and multi-level line encoding. Pulse amplitude modulation (PAM) and pulse coded modulation (PCM). Inter-symbol interference (ISI) and Nyquist theorem, Nyquist pulses. Noise and error probability in binary and multilevel PAM transmission. Matched filter and corresponding error probability.

• Passband digital transmission
Amplitude shift keying (ASK), quadrature amplitude modulation (QAM) and phase shift keying (PSK). Transmitter and receiver scheme. Constellations and distance between symbols. Symbol energy.

• Channel capacity and encoding
Second Shannon theorem. Channel capacity and encoding. Hard decoding and Hamming distance.

C. Prati, Segnali e sistemi per le telecomunicazioni