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: 

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