Signals and Systems — Winter 2023

Define continuous and discrete signals..

Find the fundamental time period of the signal:1 x ( t ) 3 s in ( 2 0 0 t )  =04

Find the even and odd components of the signal: x ( t ) = 1 + 2 t + 6 t 2 + 4 t 5 + 4 t Explain the classification of signals.

Explain the classification of systems.

Explain the properties of Linear Time Invariant Systems.

Represent the following signals graphically. ( ) (1) x(n) = 1,0,1,01,0 (2) x ( t ) = u ( t + 1 )07

Find the convolution of the following signals. ( ) ( ) x (n) = 1,0,3,4,3 and x (n) = 0,1,3,1,812

Derive the relationship between fourier and laplace transform.

Explain the properties of convolution.

Find the Fourier series expansion of the half wave rectified sine wave as shown in figure below: A 0 𝜋 2π 3π t

Q. 3 (a) Find the step response of the system whose impulse response is given as h ( t ) = u ( t + 1 ) − u ( t − 1 )03

Explain the properties of Fourier Transform.

Obtain the Fourier Transform of following signals: (1) x(t)=eatu(t) (2) x(t) =1

.Explain the initial and final value theorem with respect to z-transform

Determine the constants of trigonometric fourier series.

Determine if the following system described by y[n]=x[n-2] is memory-less , causal, linear, time invariant.

Define z-transform.

Explain the properties of z-transform.

Define Region of convergence. Explain the properties of RoC.

Explain the case study of signals in communication field.

Describe the conditions of existence of fourier transform.

Determine the z-transform of following signals.2 ( (1 ) x ) x ( n ( n ) ) = =2 ( u 0 . (6 n ) + n u2 ( ) n ) + ( 0 . 9 ) n u ( n )07

Determine the inverse z-transform by power series expansion: X ( z ) = 1 −1 a z − 103

Determine the inverse z-transform by partial fraction expansion method: (z+2) X(z) = 2z2 −7z+3

Explain the applications of digital signals in biomedical field.