Trouble trying to plot the output of an input signal with an impulse response

Here is my code where I took the convolution of an input signal x(t) and the impulse response h(t). I took the laplace of each signal and multiplied those laplace values. My problem is trying to plot the impulse response. I tried to define t from 0 - 10 seconds with a dt of 0.01, but this would error out when I tried to find my Laplace results for X(s) and H(s), so I removed it and it worked fine. However, I am not sure how to plot the impulse response and output response y(t) without a defined t value? Any help would be greatly appreciated. Here is my code:

syms t s;

>> x = (5/7)*exp(-t) - (12/7)*exp(-8*t); % x = x(t)

>> h = cos(2*t) + 4*sin(2*t); % h = h(t)

>> % Define the Laplace of the impulse function h(t) = cos(2t) + 4sin(2t)

>> H = laplace(cos(2*t) + 4*sin(2*t)); % H = H(s)

>> pretty(H)

s 8

------ + ------

2 2

s + 4 s + 4

% Define the Laplace of the input function x(t) = (5/7)e(-t) - (12/7)e(-8t)

>> X = laplace((5/7)*exp(-t) - (12/7)*exp(-8*t)); % X = X(s)

>> pretty(X)

5 12

--------- - ---------

7 (s + 1) 7 (s + 8)

% Define Y(s) as the convolution of x(t) * h(t) = X(s) x H(s)

Y = X*H; % Y = Y(s)

pretty(Y)

/ 5 12 \ / s 8 \

| --------- - --------- | | ------ + ------ |

\ 7 (s + 1) 7 (s + 8) / | 2 2 |

\ s + 4 s + 4 /

% Define the Inverse Laplace of Y(s) = [(5/(7(s + 1))) - (12/(7(s + 8)))]*[(s/(s^2 + 4) + (8/(s^2 + 4)]

y = ilaplace(Y); % y = y(t)

pretty(y)

exp(-t) - cos(2 t)

subplot(312)

plot(t,x);

Error using plot

Data must be numeric, datetime, duration or an array convertible to double.

Answer 1

[Star Strider]

Use the fplot function —

syms t s;
x = (5/7)*exp(-t) - (12/7)*exp(-8*t); % x = x(t)
h = cos(2*t) + 4*sin(2*t); % h = h(t)
% Define the Laplace of the impulse function h(t) = cos(2t) + 4sin(2t)
H = laplace(cos(2*t) + 4*sin(2*t)); % H = H(s)
% pretty(H)
H

H = 

% Define the Laplace of the input function x(t) = (5/7)e(-t) - (12/7)e(-8t)
X = laplace((5/7)*exp(-t) - (12/7)*exp(-8*t)); % X = X(s)
% pretty(X)
X

X = 

% Define Y(s) as the convolution of x(t) * h(t) = X(s) x H(s)
Y = X*H; % Y = Y(s)
% pretty(Y)
Y

Y = 

% Define the Inverse Laplace of Y(s) = [(5/(7(s + 1))) - (12/(7(s + 8)))]*[(s/(s^2 + 4) + (8/(s^2 + 4)]
y = ilaplace(Y); % y = y(t)
% pretty(y)

subplot(312)
fplot(x, [0 10]);
grid

.

[Anthony Walden]

Thank you for the assist, that helped tremendously!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

Answer 2

[tedros]

how to find the out put y(t) of a state matric