What is the difference in the shown waveforms conceptually?

  1. Hi guys ,
    My present doubt is regarding the waveforms shown in the image. The first plot is a impulse train. what is the difference having δ(t) in one plot and 1 at t=0, (0 else where) in a second case. whether time or frequency is the case...
     

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  2. jcsd
  3. Simon Bridge

    Simon Bridge 14,816
    Science Advisor
    Homework Helper
    Gold Member

    You mean the difference between a train of shifted delta functions and that of unit spikes?

    In the second one, at t=0, f(t)=1. In the first one, f(t=0) is undefined.
    It will probably help you understand if you consider the situations you'd have to find the area under the train in each case ... or do a fourier transform.
     
  4. Sir , thanks for the eye opener............ But how does this concept do apply practically.........for example when viewing spectrum analyzer of a periodic signal, the frequency domain we see is what mathematically?Is it impulse functions or spikes...? How do we treat this impulses practically?
     
  5. Baluncore

    Baluncore 2,580
    Science Advisor

    A spectrum analyser cannot represent infinite pulses of zero width so we see each as a limited amplitude pulse with an area determined by energy. A train of Dirac delta pulses is a Dirac comb.
    The spectrum of a Dirac comb is itself a Dirac comb.
    Take a look at... https://en.wikipedia.org/wiki/Dirac_comb
     
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