signals & systems
Semester : IV
Course Code : 18EC45
CIE Marks : 40 SEE Marks : 60
Module – 1
Hand Written Notes
Module – 2
Module – 3
Module – 4
SIGNALS & SYSTEMS
Introduction and Classification of signals: Definition of signal and systems, communication, and control system as examples Classification of signals.
Basic Operations on signals: Amplitude scaling, addition, multiplication, differentiation, integration, time scaling, time shift, and time reversal.
Elementary signals/Functions: Exponential, sinusoidal, step,impulse and ramp functions. Expression of triangular, rectangular and other waveforms in terms of elementary signals.
System Classification and properties: Linear-nonlinear, Time variant-invariant, causal-noncausal, static-dynamic, stable-unstable, invertible.
Time-domain representation of LTI System: Impulse response, convolution sum, convolution integral. Computation of convolution sum and convolution integral using the graphical method for unit step and unit step, unit step and exponential, exponential and exponential, unit step and rectangular, and rectangular and rectangular.
LTI system Properties in terms of impulse response: System interconnection, Memoryless, Causal, Stable, Invertible and Deconvolution, and step response.
Fourier Representation of Periodic Signals: CTF Properties and basic problems.
Fourier Representation of aperiodic Signals: Introduction to Fourier Transform & DTFT, Definition and basic problems.
Properties of Fourier Transform: Linearity, Timeshift, Frequency shift, Scaling, Differentiation and Integration, Convolution and Modulation, Parseval’s theorem and problems on properties of Fourier Transform.
The Z-Transforms: Z transform, properties of the region of convergence, properties of the Z-transform, Inverse Z-transform, Causality and stability, Transform analysis of LTI systems.