Digital signal processing systems. Advantages. 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-phas