Laplace  Transforms

Aim: To perform waveform synthesis using Laplace Transforms of a given signal 

Equipment: PC with windows (95/98/XP/NT/2000).

                       MATLAB Software

Program:

Program for Laplace Transform:

f=t

syms f t;

f=t;

laplace(f)

 

Program for inverse Laplace Transform
 

f(s)=24/s(s+8)                       inverse LT

syms F s

F=24/(s*(s+8));

ilaplace(F)

y(s)=24/s(s+8)                    inverse LT poles and zeros

 

Signal syntheses using Laplace Transform for Triangular input:

clear all

clc

t=0:1:5

s=(t);

subplot(2,3,1)

plot(t,s);

u=ones(1,6)

subplot(2,3,2)

plot(t,u);

f1=t.*u;

subplot(2,3,3)

plot(f1);

s2=-2*(t-1);

subplot(2,3,4);

plot(s2);

u1=[0 1 1 1 1 1];

f2=-2*(t-1).*u1;

subplot(2,3,5);

plot(f2);

u2=[0 0 1 1 1 1];

f3=(t-2).*u2;

subplot(2,3,6);

plot(f3);

f=f1+f2+f3;

figure;

plot(t,f);

% n=exp(-t);

% n=uint8(n);

% f=uint8(f);

% R = int(f,n,0,6)

laplace(f);

Output: 

Output
Input

Result: In this experiment the Triangular signal synthesized using Laplace Transforms using MATLAB.

  • Created
    Dec 09, 2019
  • Updated
    Dec 09, 2019
  • Views
    150
You May Like

Introduction

Basic operations on Matrices

Genaration of various signals and sequences

Operations on signals and sequences 

Finding the even and odd parts of signal/sequence and real and imaginary parts of signal

Verification of Linearity and time in-variance  properties of a given continuous/discrete system

Linear Convolution

Auto correlation and cross correlation between signals and sequences 

Computation of unit sample, unit step and sinusoidal response of  the given LTI system and verifying  its physical reliability and stability properties 

GIBBS phenomenon 

Sampling theorem verification

Finding the Fourier transform of a given signal and plotting its magnitude and phase spectrum 

Laplace  Transforms

Locating the zeros and poles and plotting the pole zero maps in z-plane for the given transfer function 

Gaussian  Noise

 Verification of Wiener- Khinchin relation 

Removal of noise by auto-correlation/cross-correlation

Extraction of Periodic  signal masked by noise using correlation.

Checking a Random process for stationarity in wide sense

To find a mean and variance of a discrete random variable 

To find a moment generating function of a discrete random variable 

Computation of Energy of sinusoidal signal

Computation of energy of rectangular pulse

Computation of  Average Power

Waveform Synthesis

Find and plot the cumulative distribution and probability density functions of a random variable

Verification of central limit theorem