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

Discussion in 'Homework Help' started by u-will-neva-no, Jan 4, 2012.

1. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2
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!

2. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
718
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.

u-will-neva-no likes this.
3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
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°

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4. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2
Thank you very much both of you!