Signals and Systems — Summer 2025

Define a signal and explain the types of signals.

Discuss the properties of continuous-time and discrete-time signals.04

Describe the significance of linearity and time-invariance in system engineering.07

Define the impulse function and its properties.

Discuss the concept of convolution in the context of continuous-time and discrete- time signals.

Compute the convolution of the following continuous-time signals: x1(t) =1,0≤t <3 0, otherwise x2(t) = 1, 0≤t <1 0,otherwise Show all the steps of the calculation.

Use convolution to determine the output of the given LTI system for the given input x[n]: Show all the steps of the calculation. x[n]={1,2,1,2} and impulse response h[n]={2,1,2,1}.

Derive the Fourier transform of the given continuous-time signal: x(t) =e−atu(t)

Describe the concept of Fourier series and its application in representing periodic signals. Provide a numerical example to illustrate the Fourier series expansion.

Discuss the method to solve difference equation using Ztransform

Define the z-transform and ROC

Prove any two properties of the z-transform.

Find the inverse Ztransform of the given discrete-time system represented by the transfer function using long division. H(z) =z/(z−0.5)

Define the Laplace transform and discuss its advantages.

Derive the Laplace transform of the given continuous-time signal: x(t) = sin{at}u(t) Show all the steps of the calculation.

07 x(t)=t for 0≤t <2 0,otherwise Determine the signal's energy and power.1

Define Nyquist rate and explain how to avoid aliasing.

For signal frequency of 1KHz find sampling frequency

State and prove sampling theorem, with all necessary equations and diagrams

Find DTFT of sequence x[n]={1,2,1,1}

Prove any two property of DTFT

Prove convolution property of Z -transform

Define periodicity of continuous and discrete time signal

Differentiate between digital and analog frequency

Check Linearity, Causality and Time invariance properties of system Y=mx+c