Frequency response Output y(t)

Discussion in 'Homework Help' started by need_help, Sep 21, 2009.

  1. need_help

    Thread Starter New Member

    Sep 7, 2009
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    f (t) = 5+4e^(j2t) + 4e^(-j2t)

    H(ω) = (1+jω) / (2+jω)

    Determine the steady-state output y(t) of the system H(ω) and express it as a real valuued signal

    HINT: Use rule : e^(jωt) ---->LTI---> H(ω)e^(jωt)

    any ideas???
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    What's LTI stand for?
     
  3. need_help

    Thread Starter New Member

    Sep 7, 2009
    23
    0
    LTI = linear time invariant
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    782
    I'd use a rather basic approach

    1. Realize that e^(j2t)+e^(-j2t) = 2 cos(2t)

    2. The input f(t) is therefore a DC shifted sinusoidal function

    3. H(0) = 0.5 for the DC component (i.e. you get half of the input DC value at the output)

    4. H(2) = (1+j2)/(2+j2) for the AC component. Or H(2) = 0.75 + j0.25 - which will produce an attenuated version of the AC component with a phase lead.

    and so on .....

    Eventually the answer would be

    v(t) = 2.5 + cos(2t+atan(1/3))

    Hope this gives some insight anyway.
     
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