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Homework Help: Sketch and mathematically represent pdf of given signal

  1. Jul 15, 2015 #1
    1. The problem statement, all variables and given/known data
    I've been asked to sketch and mathematically represent the pdf of 2 signals:

    (a) rep2T{5 rect(t/T) - rect((t-T)/T)}
    (b) rep2T{2 rect(t/T) + 4Arect(2t/T)}

    A(t) is the lambda function
    A(t) = 1- t for 0 <= t <= 1
    1+t for -1 <= t <= 0

    Any help would be much appreciated!

    2. Relevant equations
    I understand how to sketch the signals itself. However, how can I derive the pdf of the function?

    3. The attempt at a solution
    The sketched signal is :
    (a) 2T period form with a 5V amplitude rectangular lasting for 1T and -1V amplitude rectangular one lasting also for 1T.
    (b) A 1T zero pulse, followed by a triangular waveform(amp = 4V) with a rect base( amp = 2V) [i.e waveform goes from 0V to 6V], the latter waveform lasts for 1T as well.

    However, how I do I derive the pdf from this?
  2. jcsd
  3. Jul 15, 2015 #2


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    Usually, the pdf is a function which looks a good deal like the function itself, but integrates to 1 over the entire domain. In this case, you would want to define it over one period.
    What do the current forms integrate to? How would you appropriately scale them so the integral becomes 1 over the period?
  4. Jul 16, 2015 #3

    rude man

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    I think you want to graph voltage v on the x axis and dp/dv on the y axis, where p is the probability that v lies between v and v + dv.
    Not sure though - what is your idea of "pdf"?
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