# find the output signal from the output signal and the frequency response

#### u-will-neva-no

Joined Mar 22, 2011
230
Hello again, I definitely need help on this question!

I have to find the output signal and the output signal and the frequency response have been given:

Input signal: $$V(t) = 10sin(4 \sqrt{3}.t)$$

Frequency response function: $$H(jw) = \frac{1}{4-jw}$$

I was looking at my notes and noticed this formula:
$$y(t)=\int ^\infty_\infty x(\tau)h(t-\tau) d\tau$$

and: $$H(jw) = \int^\infty_\infty h(t)exp(-jwt) dt$$
(limits should be - infinity for the value of b on both integral limit)

Normally I would write my method but I'm not sure how to use the above formulas..They may even be the wrong formula to use.

thanks for reading and I look forward to your help as always!

#### thatoneguy

Joined Feb 19, 2009
6,359
You can get the -∞ using braces {} around the relevant part:

H(jw) = \int^\infty_{-\infty}

results in:

$$H(jw) = \int^\infty_{-\infty}$$

Sorry I can't help with the filter part at the moment, I just try to make posts look good.

You'd use the second of your integrals H(jω), not the first integral. Once you think you have an answer, try plotting the output.

#### t_n_k

Joined Mar 6, 2009
5,455
At ω=4√3

$$H_{(j\omega)}=\frac{1}{(4-4\sqr(3)j)}=0.125 \angle {60^o}$$

Hence the input signal amplitude is modified by a factor of 0.125 and the phase angle shifted by 60°