ANALOG CIRCUITS AND ALGORITHMS FOR STATISTICAL SIGNAL PROCESSING
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- Versione italiana
- Academic year
- 2015/2016
- Teacher
- GIANLUCA SETTI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- ING-IND/31
Training objectives
- The aim of the course is to demonstrate how some instruments for the analysis of the stochastic process that model or are generated from some circuits or complex dynamical systems can be profitably employed for signal transmission and processing using electronic circuits. To reach such a goal several concept will be introduced which grounds estimation theory, and which will be employed for evaluating the performance of the principal spectrum evaluation techniques.
The main knowledge acquired ad the end of the class is:
- capability to analyze an electronic circuit/system, with periodic, multiperiodic or chaotic behavior;
- properties of a chaotic signal both from a deterministic and stocastich point of view;
- ergodic, mixing and exact property of a chaotic system;
- methods for random number generations;
- methods for EMI reduction based on spread spectrum clocking
- methods for signal acquisition based on compressed sensing
The principal skills (in terms of capabilities of applying the knowledge acquired) are:
- Design of circuits able to generate signals with desired statistical features;
- Co-Design electronic circuits/systems and related algorithms Prerequisites
- It is necessary to possess knowledge of the following topics from the classes of “Fundaments of Automatics”, “Geometry and Algebra” “Statistical Methods for Engineering” and “Mathematical Analysis II”:
- Stability Theory, poles of a transfer functions;
- matrices, vectors and elementary operations, linear systems and their solutions;
- solutions of systems of differential equations of first order;
- random variables and probability density. Course programme
- 1. Dynamics of Complex dynamical systems
Generality: Systems of nonlinear differential equation: fundamental theorems, geometrical interpretations; Classifications of asymptotic behaviors (Equilibrium points, definitions and methods for studying their stability; Periodic behavior: limit cycles e fundamental theorems, Floquest multipliers and stability; Non periodic behavior: toroidal and chaotic attractors); Principal investigations methods (Poincarè maps and time-domain analysis); Principal bifurcations phenomena (saddle-node of equilibrium points, period doubling, flip, fold, flip-fold)
Applications: Circuits with piecewise nonlinearity: Chua's circuit; 3-points oscillators: Colpitts oscillators and his advanced design criteria.
2. Statistical dynamis for discrete-time systems
Generality: Ergodicity - mixingness - exactness; Perron-Frobenious operator and his properties; State quantized case and projection of the PF operator (Equivalence with Markov chains, Kalman embedding procedure, Time-Markov systems)
Applications: Control of the correlation profile/power spectral density (general concepts, control of base-band correlations with a family of parametric maps; Control of pass-band correlations and stochastic frequency modulation); Applications to optimization of DS-CDMA (single user receiver, with and without fading), to reduction of EMI due to timing signals (clock, PWM for class-D amplifiers)
3. Power spectral density
Energy and power density spectrum (PDS); Wiener-Khinchin theorem; PDS and samples; the problem of spectrum estimation; basic concepts in estimation theory; PDS estimation with a periodogram (polarization, non-consistency, modified periodogram); minimum variance PSD estimation (correlation estimation). Didactic methods
- The course is organized as follows:
- lectures on all subjects of the course;
- classroom exercises related to the theoretical arguments entitling finding the solution of circuits with increasing complexity;
- laboratory experiments (where students are divided in groups) having as subject the measurement of the characteristics of a two-ports and the measurement of the transient behavior in an RC circuit. Learning assessment procedures
- The final examination is in oral form with questions on the topics of the course, the student can submit a brief report on a project whose theme is assigned by the teacher this replaces two questions.
Passing the final exam is the proof that knowledge and abilities outlined in the training objectives of the course have been achieved. Reference texts
- Professor's handouts
