Digital Signal Processing and Laboratory
*) Knowledge and understanding: Knowledge of the mathematical foundations for the representation, analysis and digital processing of signals. Knowledge of design methods of FIR and IIR filters. Knowledge of classical and Bayesian statistical estimation techniques.
*) Applied knowledge and understanding: analysis of a signal in the frequency domain, design of a digital filter, performing digital filtering of signals, statistical estimation of parameters from noisy data.
*) Making judgments: developing the ability to critically and synergistically use various tools for numerical processing and statistical estimate of signals. Knowing how to evaluate the design constraints of a processing system in terms of error, computational complexity and stability of the algorithm.
*) Communication skills: Ability to present the topics in a clear and rigorous technical-scientific point of view. Knowing how to submit an application solution in a simple and comprehensive.
*) Learning skills: knowing how to integrate knowledge from various sources for the purpose of deepening. Knowing how to use the concepts covered for applications other than those disclosed.
For the successful achievement of objectives, the knowledge of signals and systems theory is required.
Digital signal processing systems. Advantages of Digital over Analog signal processing. Continuous-Time and Discrete-Time signals. Continuous-Valued and Discrete-Valued signals. Deterministic and random signals. Sinusoidal signals. Harmonically related complex exponentials. Analog-to-Digital and Digita-to-Analog conversion. Sampling of analog signals. The Sampling Theorem. Quantization. Quantization of sinusoidal signals. Coding of quantized samples. Digital-to-Analog conversion. Some elementary discrete-time signals. Classification of discrete-time signals. Manipulations of discrete-time signals.
Discrete-Time systems. Input-Output description. Block diagram representation of discrete-time systems. Classification and interconnection of discrete-time systems. Analysis of discrete-time Linear Time-Invariant (LTI) systems. Response of LTI Systems: the Convolution Sum. Properties of convolution and the interconnection of LTI systems. Causal LTI systems. Stability. Systems with finite-duration and infinite-duration impulse response.
Discrete-Time systems described by difference equations. Recursive and nonrecursive discrete-time systems. LTI systems characterized by constant-coefficient difference equations. Solution of linear constant-coefficient difference equations. The ompulse response of an LTI recursive system. Implementation of discrete-time systems. Structures for the realization of LTI systems. Recursive and nonrecursive realizations of FIR systems. Crosscorrelation and autocorrelation sequences. Properties of the autocorrelation and crosscorrelation sequences. Correlation of periodic sequences. Computation of correlation sequences. Input-Output correlation sequences.
The z-Transform. The direct and inverse z-Transform. Properties of the z-Transform. Poles and Zeros. Pole location and time-domain behaviour for causal signals. The System Function of an LTI system.
The Discrete Fourier Transform (DFT). The DFT as a linear transformation.
Properties of the DFT. Frequency analysis of signals using the DFT.
Design of digital filters. Causality and its implications. Characteristics of practical frequency-selective filters. FIR and IIR filters Applications. Zeros of linear phase filters: COMB Filters. Notch Filters. Design of FIR filters. Symmetric and antisymmeiric FIR filters. Design of linear-phase FIR filters using Windows. Design of linear-phase FIR filters by the frequency-sampling method. Design of optimum equiripple linear-phase FIR filters. Design of IIR filters from analog filters. IIR filter design by approximation of derivatives.
Theory of statistical estimation. The mathematical problem of the estimate. Classical estimation theory. Biased estimators. Minimum variance estimators. MVU estimators. Extension to the vector case. Cramer-Rao Bounds. CRLB for signals in AWGN. Transformation of parameters. Extension to the vector case. CRLB for the general Gaussian case. Examples of Signal Processing. Linear models. Generalized linear models. Maximum likelihood estimators. Properties of ML estimators. MLE for transformation of parameters. Extension to the vector case. MLE numerical determination. Asymptotic properties of the ML estimators. Least squares. Linear case. Bayesian estimation. Bayesian cost. Bayesian risk. MMSE estimators. MAP estimators. Bayesian Gaussian case. Iterative methods. Global minimization. A priori information.
Digital signal processing systems. Digital signals. Sampling and quantisation.
Discrete time systems and their properties. Response of LTI systems. FIR and IIR systems.
Discrete time systems described by difference equations. Realization of discrete LTI systems.
The direct and reverse Zeta transform and properties. The system function of an LTI system.
Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT).
Design of digital filters.
Theory of Statistical Estimation. MVU estimators. Maximum likelihood estimators.
Least square estimation.
Bayesian estimate. MMSE and MAP estimators.
The course consists of a series of lectures and practical computer exercises carried out in Matlab.
J. G. Proakis, D. G. Manolakis . Digital Signal. Processing. Principles, Algorithms, and Applications. Prentice Hall.
S. M. Kay. Fundamentals of Statistical Signal Processing: Estimation Theory(Vol. 1). Prentice Hall
S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory,(Vol. 1), Prentice Hall, 1993,
The final examination consists of an oral interview with the aim of assessing the knowledge acquired, the ability of understanding and the oral presentation. At the oral interview it is necessary to present a short written report on the exercises carried out in Matlab in the laboratory during the course. The interview will cover all the topics treated in the course and the discussion of the exercises.