Introduction and Classification of signals:Definition of signal and systems, communication and control systems as examples. Sampling of analogsignals, Continuous time and discrete time signal, Classification of signals as even, odd, periodic and non-periodic, deterministic and non-deterministic, energy and power.Elementary signals/Functions: exponential, sine, impulse, step and its properties, ramp, rectangular, triangular, signum, sync functions.Operations on signals: Amplitude scaling, addition, multiplication, differentiation, integration(Accumulator for DT), time scaling, time shifting and time folding.Systems: Definition, Classification: linear and nonlinear, time variant and invariant, causal and noncausal, static and dynamic, stable and unstable, invertible.
Time domain representation of LTI System: System modeling: Input-output relation, definition of impulse response, convolution sum, convolution integral,computation of convolution integral and convolution sum using graphical method for unit step to unit step, unit step to exponential, exponential to exponential, unit step to rectangular and rectangular to rectangular only. Properties of convolution.
System interconnection, system properties in terms of impulse response, step response in terms of impulse response.Fourier Representation of Periodic Signals:Introduction to CTFS and DTFS, definition, properties (No derivation) and basic problems (inverse Fourier series is excluded).
Fourier Representation of aperiodic Signals:FT representation of aperiodic CT signals - FT, definition, FT of standard CT signals, Properties andtheir significance.FT representation of aperiodic discrete signalsDTFT, definition, DTFT of standard discrete signals,Properties and their significance,Impulse sampling and reconstruction: Samplingtheorem (only statement) and reconstruction of signals.
Z-Transforms: Introduction, the Z-transform, properties of the Region of convergence, Properties ofthe Z-Transform, Inversion of the Z-Transform, Transform analysis of LTI systems.