# Frequency response using fourier

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

• Is this homework? – Phonon Nov 20 '13 at 4:01
• kinda, he asked us to solve it but we dont have to turn it in however i want to learn how to do it – user998316 Nov 20 '13 at 19:09
• 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. – Dilip Sarwate Dec 21 '13 at 19:54

## 2 Answers

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.

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 $h(t)=e^{-3t}u(t)$