-1
$\begingroup$

i need to find the frequency response of the following equations:

$$h(t) = e^{-3t} u(t)$$ $$x(t) = 1+\cos\left(\frac{4\pi}{3}t\right)$$

find $y(t)$

However i am quite confused on how to do this, please explain and show every step so i can learn

$\endgroup$
  • $\begingroup$ Is this homework? $\endgroup$ – Phonon Nov 20 '13 at 4:01
  • $\begingroup$ kinda, he asked us to solve it but we dont have to turn it in however i want to learn how to do it $\endgroup$ – user998316 Nov 20 '13 at 19:09
  • $\begingroup$ Equations don't have frequency responses; systems do. You need to say what, if any, is the relationship between the desired output $y(t)$ and the givens $x(t)$ and $h(t)$. Please edit to add this information if your instructor gave it to you, and if he did not, ask your instructor for this information. -1 for now, pending edits. $\endgroup$ – Dilip Sarwate Dec 21 '13 at 19:54
1
$\begingroup$

You have to calculate $H(f)$, the Fourier transform of $h$. Similarly, you have to calculate $X(f)$ which is FT of $x$. Then, recall that, convolution in time domain is multiplication in frequency domain. Using this property, you will get $Y(f)$. Take inverse Fourier transform.

Since this is probably a HW, I will not give further details, the general way is like that. You can manage algebra.

$\endgroup$
0
$\begingroup$

Hint #1: look up the definition of signals and systems. "Calculating the frequency response" and "finding y(t)" which presumably is x convolved with h are two different things.

Hint #2: This looks like a typo. It's most likely $h(t)=e^{-3t}u(t)$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.