Signals and Systems syllabus

Representation of Continuous and Discrete-time Signals, Unit Step, Unit Ramp, Unit Impulse, Sinusoidal and Complex Exponentials. Classification of signals – Periodic and Aperiodic Signal, Even and Odd Signal, Energy and Power Signal, Deterministic and Random signals. Transformation of Independent Variables –Time Shifting, Time Scaling and Time Reversal.

Representation of Continuous and Discrete Time Systems. Classification of systems - Static and Dynamic, Linear and Nonlinear, Time variant and Time Invariant, Causal and Non–Causal, Stable and unstable, Invertible and non- invertible systems. Block Diagram Representation and Interconnection of Systems Continuous-Time LTI Systems: The Convolution Integral, Discrete-Time LTI Systems: The Convolution Sum. Properties of Linear Time-Invariant Systems.

Fourier Series Representation of Continuous-Time Periodic Signals, Convergence of the Fourier Series, Properties of Continuous-Time Fourier Series, Dirichlet condition for existence of Fourier series, orthogonality, basis functions, Magnitude and phase response. Fourier Transform (FT) representation of Continuous-Time Aperiodic signals, Dirichlet condition for existence of Fourier transform, Properties of Continuous-Time Fourier Transform, Magnitude and phase response, FT of standard Continuous-Time signals.

Definition of Laplace Transform (LT), Limitations of Fourier transform and need of Laplace transform, ROC, Laplace transform of standard periodic and Aperiodic functions, properties of Laplace transform and their significance, Laplace transform evaluation using properties, Inverse Laplace transform based on partial fraction expansion, stability considerations in S-domain, Application of Laplace transform to the LTI system analysis.

Z-Transform, Significance and Properties of Region of Convergence, Properties of Z-Transform, Inverse Z Transform, relationship of Z-transform with Fourier transform, applications of Z- transform to solutions of difference equations.