Classification of signals Continuous-time signal and discrete-time signals periodic and aperiodic signals even and odd signals energy and power signals deterministic and random signal. Basic operations on signals arithmetic operations reflections time shifting time scaling. Types of signals exponential, sinusoidal, step, impulse and ramp. System - impulse response of the system. Classification of systems stable memory invertible time invariant linear causal. Convolution integrals and its properties. Sampling theorem.
Fourier Series and Fourier Transform
Continuous-time Fourier series (CTFS) Exponential and trigonometric representation of CTFS. Dirichlet condition. Properties of CTFS linearity, time-shifting, time-reversal, time-scaling, multiplication, Parseval's relation differentiation integration. Continuous-time Fourier transform (CTFT) properties of CTFT linearity, time shifting, time-reversal, time-scaling, multiplication, convolution, Parseval's relation differentiation in time and frequency domains integration. Application to systems - solution to differential equation using CTFT. Discrete-time Fourier series (DTFS) and Discrete-time Fourier transform (DTFT) properties linearity, time-shifting, time-reversal, time-scaling, multiplication, Parseval's relation difference accumulation. Application to systems - solution to difference equation using DTFT.
Laplace Transform
Unilateral and bilateral Laplace transform (LT) region of convergence (ROC) - properties of LT linearity, time-shifting, time-reversal, time-scaling, multiplication, convolution, Parseval's relation differentiation in time and frequency domain integration initial value and final value theorem inversion of LT solution to differential equation using LT analysis of passive network using LT.
Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)
Discrete Fourier transform properties of DFT linearity, circular-shifting in time and frequency domains, time-reversal, time-scaling, circular correlation, multiplication, convolution, parseval's relation circular convolution circle method, matrix method sectional convolution overlap-add method and overlap-save method radix-2 fast Fourier algorithm decimation-in-time FFT decimation-in-frequency FFT inverse FFT.
Z-tranform and state matrix
Z-transform (ZT) region of convergence (ROC) - properties of ZT linearity, time-shifting, time-reversal, time-scaling, multiplication, convolution, parseval's relation differentiation in time and frequency domain integration initial value and final value theorem inversion of ZT power series method, partial-fraction method, residual method - solution to difference equation using ZT.State variable description for LTI system determination of transfer function from state model discrete-time model.
REFERENCE
Text Books
Allan V. Oppenhein et al, Signals and Systems, Pearson Education, 2007
Reference Books
1. Simon Haykin and Barry Van Veen, Signals and Systems, John Willey, 1999
2. Roger E. Zeimer et al, Signals and Systems, McMillan, 2nd Edition, 1999.
3. Douglas K. Linder, Signals and Systems, McGraw-Hill, 2nd Edition, 1999