Signals and Systems(ECE 2-1)

(15A04303) SIGNALS AND SYSTEMS

Course objectives:

• To study about signals and systems.
• To do analysis of signals & systems (continuous and discrete) using time domain & frequency domain methods.
• To understand the stability of systems through the concept of ROC.
• To know various transform techniques in the analysis of signals and systems.

Learning Outcomes:

• For integro-differential equations, the students will have the knowledge to make use of Laplace transforms.
• For continuous time signals the students will make use of Fourier transform and Fourier series.
• For discrete time signals the students will make use of Z transforms.
• The concept of convolution is useful for analysis in the areas of linear systems and communication theory.

Syllabus

UNIT I

SIGNALS & SYSTEMS: Definition and classification ofSignal and Systems (Continuous time and Discrete time),Elementary signals such as Dirac delta, unit step, ramp, sinusoidal and exponential and operations on signals.Analogy between vectors and signals-orthogonality-Mean Square error-Fourier series: Trigonometric & Exponential and concept of discrete spectrum

UNIT II

CONTINUOUS TIME FOURIER TRANSFORM: Definition, Computation and properties ofFourier Transform for different types of signals. Statement and proof of sampling theorem of low pass signals

UNIT III

SIGNAL TRANSMISSION THROUGH LINEAR SYSTEMS: Linear system, impulse response, Response of a linear system, linear time-invariant (LTI) system, linear time variant (LTV) system, Transfer function of a LTI system. Filter characteristics of linear systems. Distortion less transmission through a system, Signal bandwidth, system bandwidth, Ideal LPF, HPF and BPF characteristics, Causality and Poly-Wiener criterion for physical realization, Relationship between bandwidth and rise time. Energy and Power Spectral Densities

UNIT IV

DISCRETE TIME FOURIER TRANSFORM: Definition, Computation and properties ofFourier Transform for different types of signals. 

UNIT-V

LAPLACE TRANSFORM: Definition-ROC-Properties-Inverse Laplace transforms-the S-plane and BIBO stability-Transfer functions-System Response to standard signals-Solution of differential equations with initial conditions.

The Z–TRANSFORM: Derivation and definition-ROC-Properties-Linearity, time shifting, change of scale, Z-domain differentiation, differencing, accumulation, convolution in discrete time, initial and final value theorems-Poles and Zeros in Z -plane-The inverse Z-Transform-System analysis-Transfer function-BIBO stability-System Response to standard signals-Solution of difference equations with initial conditions.

Study Material's For Signals & Systems

2 Mark's for 5 Units: Download

Lecture Notes for 5 Units(Suggested): Download

Text Book- Linear Systems & Signals: Download

Unit Wise

Unit-II:

Continuous-Time Fourier Transform: Download

Unit-III:

Signal Transmission Through Linear Systems: Download

Unit-IV:

Discrete Time Fourier Transform: Download

Unit-V:

Laplace Transform Formulae's: Download

Laplace Transform Properties: Download

Z-Transform Properties: Download

Z-Transform Formulae's: Download