Signals & Systems Lab 7

Aim

To compute laplace and inverse laplace using matlab with function and without

clc;
 
clear all;
 
close all;
 
syms t s;
 
% Define the functions
 
x1 = exp(-2*t) * heaviside(t);
 
x2 = exp(-2*t) * heaviside(t);
 
x3 = exp(-2*t) * heaviside(t) + exp(-4*t) * heaviside(t);
 
x4 = exp(-2*t) * heaviside(t) - exp(-4*t) * heaviside(t);
 
% Perform Laplace transforms
 
X1_s = laplace(x1, t, s);
 
X2_s = laplace(x2, t, s);
 
X3_s = laplace(x3, t, s);
 
X4_s = laplace(x4, t, s);
 
% Perform Inverse Laplace transforms (just for demonstration)
 
inv_X1 = ilaplace(X1_s, s, t);
 
inv_X2 = ilaplace(X2_s, s, t);
 
inv_X3 = ilaplace(X3_s, s, t);
 
inv_X4 = ilaplace(X4_s, s, t);
 
% Display the results
 
disp('Laplace Transform of x1(t):');
 
disp(X1_s);
 
disp('Inverse Laplace Transform of x1(s):');
 
disp(inv_X1);
 
disp('Laplace Transform of x2(t):');
 
disp(X2_s);
 
disp('Inverse Laplace Transform of x2(s):');
 
disp(inv_X2);
 
disp('Laplace Transform of x3(t):');
 
disp(X3_s);
 
disp('Inverse Laplace Transform of x3(s):');
 
disp(inv_X3);
 
disp('Laplace Transform of x4(t):');
 
disp(X4_s);
 
disp('Inverse Laplace Transform of x4(s):');
 
disp(inv_X4);
 
% Manual
 
ml1=int(x1 * exp(-s*t), t, 0, inf);
 
ml2=int(x1 * exp(-s*t), t, 0, inf);
 
ml3=int(x1 * exp(-s*t), t, 0, inf);
 
ml4=int(x1 * exp(-s*t), t, 0, inf);
 
% Displaying Manual
 
disp(ml1);
 
disp(ml2);
 
disp(ml3);
 
disp(ml4);

Laplace Transform of x1(t): 1/(s + 2) Inverse Laplace Transform of x1(s): exp(-2*t) Laplace Transform of x2(t): 1/(s + 2) Inverse Laplace Transform of x2(s): exp(-2*t) Laplace Transform of x3(t): 1/(s + 2) + 1/(s + 4) Inverse Laplace Transform of x3(s): exp(-2*t) + exp(-4*t) Laplace Transform of x4(t): 1/(s + 2) - 1/(s + 4) Inverse Laplace Transform of x4(s): exp(-2*t) - exp(-4*t)
 
piecewise(s < -2, Inf, real(s) ~= -2 & ~in(s, 'real'), 1/(s + 2) - limit(exp(- 2*t - t*s), t, Inf)/(s + 2), angle(s) in Dom::Interval(-pi/2, pi/2) & s ~= 0 | -2 < s, 1/(s + 2), (real(s) == -2 | in(s, 'real')) & ~angle(s) in Dom::Interval(-pi/2, pi/2) & (~in(s, 'real') | s == -2), int(exp(-2*t)*exp(-t*s), t, 0, Inf))
 
piecewise(s < -2, Inf, real(s) ~= -2 & ~in(s, 'real'), 1/(s + 2) - limit(exp(- 2*t - t*s), t, Inf)/(s + 2), angle(s) in Dom::Interval(-pi/2, pi/2) & s ~= 0 | -2 < s, 1/(s + 2), (real(s) == -2 | in(s, 'real')) & ~angle(s) in Dom::Interval(-pi/2, pi/2) & (~in(s, 'real') | s == -2), int(exp(-2*t)*exp(-t*s), t, 0, Inf))
 
piecewise(s < -2, Inf, real(s) ~= -2 & ~in(s, 'real'), 1/(s + 2) - limit(exp(- 2*t - t*s), t, Inf)/(s + 2), angle(s) in Dom::Interval(-pi/2, pi/2) & s ~= 0 | -2 < s, 1/(s + 2), (real(s) == -2 | in(s, 'real')) & ~angle(s) in Dom::Interval(-pi/2, pi/2) & (~in(s, 'real') | s == -2), int(exp(-2*t)*exp(-t*s), t, 0, Inf))
 
piecewise(s < -2, Inf, real(s) ~= -2 & ~in(s, 'real'), 1/(s + 2) - limit(exp(- 2*t - t*s), t, Inf)/(s + 2), angle(s) in Dom::Interval(-pi/2, pi/2) & s ~= 0 | -2 < s, 1/(s + 2), (real(s) == -2 | in(s, 'real')) & ~angle(s) in Dom::Interval(-pi/2, pi/2) & (~in(s, 'real') | s == -2), int(exp(-2*t)*exp(-t*s), t, 0, Inf))

References

Information

• date: 2024.09.27
• time: 13:17