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. :D

    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°
     
    u-will-neva-no likes this.
  4. u-will-neva-no

    Thread Starter Member

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