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.
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CreatedDec 09, 2019
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UpdatedDec 09, 2019
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Views365
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
