Portale di Ateneo - En.Unibs.it

[Lecture/problem solving]

Detailed program - part 1

Introduction [2/2]

Communication system; information and noise; signal; energy; power; periodicity.
Signal classification and elementary operations [4/5]

Signal classification (origin, energy, shape, frequency, time); elementary operations: sum, product, shift, time-inversion, scale change; decomposition in odd and even parts. Elementary signals: rectangle, triangle, gaussian, sinusoidal signals, unit step, sign function, sinc function. Elements of distribution theory; Dirac impulse (definition and properties); Dirac train.

System classification [4/5]
Linearity, causality, memory, shift-invariance, stability. Input-output relation of linear shift invariant (LSI) systems: LSI impulse response; LSI causality and stability. Linear convolution: definition, properties, geometrical interpretation. LSI eigenfunction. LSI frequency response.

Frequency representation of signals [6/10]
Revision of complex number. Fourier transform of continuous-time signals: definition and inversion formula. Spectrum amplitude and phase spectra. Fourier transform properties. Bandwidth. Parseval identities. Fourier transform convergence. Gibbs phenomenon. Periodic signal spectrum. Fourier series: definition and properties. Asymptotic behavior and convergence of Fourier series expansion. (Energy/Power) spectral density of a signal. Unilateral frequency representations.

Vectorial representation of signals [4/5]
Revision of linear algebra. Signal space, signal distance, signal norm, inner product between signals. Schwarz inequality. Orthogonal and bi-orthogonal basis. Generalized Parseval identities. Least square approximation of signals. Complete basis examples (Walsh transform, shifted sinc families, ...). Auto-/Cross-correlation functions for energy/power/periodic signals. Convolution versus correlation. Normalized and circular convolution
.

Detailed program - part 2

Introduction to stochastic processes [6/10]
Revision of probability theory: axiomatic definition, events, incompatibility, independence, conditional events, Total probability theorem, Bayes theorem. Random variables: pdf, distribution function, expectation (mean, variance). Join random variables: joint pdf, joint distribution, joint moment
s (correlation); independence of random variables; examples. Functions of random variables. Conditional random variables: conditional pdf, conditional expected values. Repeated trials. Law of large numbers. Poisson distribution. Central Limit Theorem. Stochastic process. Stationarity and ergodicity. Auto-correlation of a random process (definition and examples, periodogram method). Power spectral density of a random process. Wiener-Khintchine theorem. Sample processes and their statistical modeling (random phase sinusoid, gaussian, PAM, ...). Noise (white, colored, narrow-band...).

Analog signal processing [4/5]
Phase and group delays; Complex envelop representation of a narrow band signal; Hilbert transform; Analytic signal. Parametric systems. Non linear systems. Ideal transmission system. Harmonic and cross-modulation distortion measures. Linear and non linear processing of a random process. Memoryless non linear processing of a random process. Linear processing of a random process. Stationary process filtering. Sum and multiplication of random processes.

Fundaments of analog and digital modulation [4/5]
Amplitude modulation (AM, DSB, SSB, VSB). Coherent demodulation and envelop demodulation. Quadrature amplitude modulation. FDM. Frequency modulation systems. Modulated signal spectrum. Demodulation with discrimination (PLL idea). Inter-symbol interference. In-band digital transmission. PAM. PAM spectrum. Main PAM codes (Manchester, AMI, ...).
Real system examples

Digital representation of an analog signal [4/5]
Analog signal sampling; frequency aliasing; reconstruction by interpolation and extrapolation (ZOH, linear interpolation, ideal interpolation). Quantization; quantization noise: statistical properties. Real A/D and D/A conversions; limit cycle of an A/D converter.

Examples of real systems using the described system components.