SYLLABUS

 

Time : 3 Hrs.                                                                                                                                         Theory : 100 Marks

Term Work : 25 Marks

 

 

 

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1.   Introduction:

1.   Definition of signal, Basic signals in continuous time and discrete time domain.  Basic operation on continuous and Discrete signal.

2.   Singular   Functions:  Ramp,  step  and  Impulse  functions,  Axiomatic,  Definition  of  impulse function, approx. to impulse function and the generalized impulse function.

3.   Classification       of   signals:       Periodic/       non-periodic, Even/Odd,       Deterministic/   Stochastic and Energy/ Power signals.

4.   Representation of a system as a mapping between input and    output      signals,       System      as      a means of transformation of signals.

5.   System  representation  in  continuous  and  discrete  time  domain  in  terms  of  differential  and difference equation respectively. Normal form representation of signals.

6.   Block diagram of continuous and Discrete time system, Classification of systems: Causal / Non- causal,  time-varying,  time-invariant,  stable/  unstable,  invertible  /  non-                                                                 invertible         and lumped/distributed                                       parameter systems.

 

2.   Linear Time Invariant System:

Continuous Time LTI system: Linear differential equations. Representation of signals by a continuum of impulses, system impulse response and the convolution integral. Evaluation and Interpretation  of Convolution Integral.

Discrete Time LTI system : Convolution sum (linear and Circular convolution). Properties of LTI

system.

 

 

3.   Laplace Transform:

Definition and its Properties,  Inverse Laplace. Transient and steady  state response of LTI system. Stability of system.

 

4.   Z-Transform:

Definition,  Convergence, properties  and  inversion  of Z-Transform. Concept of single  and  double sided Laplace Transform, Analysis of discrete time system using Z-Transform. Relationship between Laplace and Z-Transform, Fourier transforms.

 

5.   Continuous and Discrete Time Fourier Series :

Orthogonal functions: Definitions, approximations, coefficient calculation on the basis of minimum mean square error.

Fourier series : Representation of Fourier series in terms of trigonometric, exponential functions. The complex Fourier spectrum. Properties of Fourier series. Convergence of Fourier series. Gibb’s phenomenon.

 

6.   Continuous and Discrete Time Fourier Transform :

Continuous and Discrete time Fourier transform and its properties.

 

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