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.
