Signals and Systems

Continuous time and discrete time signals, periodic signals, energy and power signal, transformer of independent variables, even and odd signals, exponential and sinusoidal signal, unit impulse and unit step functions, interconnections of systems, systems with and without memory, causality, stability, linearity and time invariance.

Introduction, sampling theorem, sampling with zero order hold reconstruction of a signal from its samples, aliasing, sampling of discrete time signals, decimation and interpolation.

Introduction, discrete LTI systems, Convolution continuous time unit impulse response and convolution integral representation of LTI systems, properties of LTI systems, Stability, causal LTI system described by difference equation, singularity functions.

: Fourier series representation for continuous time periodic signals, convergence and properties of continuous time Fourier series. Fourier series representation and properties of discrete time periodic signals, Fourier series and LTI system, frequency shaping and frequency selective filters, discrete time filters.

Introduction, representation for a periodic signals, Fourier series representation of a periodic signals, convergence of Fourier transform, Fourier Transform for periodic, properties of continuous time Fourier transform, convolution and multiplication properties systems described by linear constant coefficient different equations. Introduction representation for a periodic signals, DTFT, Fourier transform for periodic signals, convergence of the Fourier transform Gibbs phenomenon, properties of discrete time Fourier transform convolution and mortification properties, system described by linear constant coefficient difference equations.

Introduction, magnetic and phase representation of Fourier transform, magnitude and phase representation of frequency response of LTI system, Linear and nonlinear phase, group delay, log magnitude plot, time domain and frequency domain aspects of non-ideal filters 1st and 2nd order continuous time and discrete time systems.