Signals - Fourier Analysis

  • Thread starter satchmo05
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  • #1
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Homework Statement



The signal y(t) is generated by convolving a band limited signal x1(t) with another band limited signal x2(t) that is y(t)=x1(t)*x2(t) where:

--> X1(jω)=0 for|ω| > 1000Π
--> X2(jω)=0 for|ω| >2000Π

Impulse train sampling is performed on y(t) to obtain:
--> yp(t)= [summation from n = (−∞,∞)] y(nT)δ(t− nT)

Specify the range of values for sampling period T which ensures that y(t) is recoverable from yp(t).

Homework Equations


All of the equations that I would are most likely showing.

The Attempt at a Solution


My thoughts were to plug in (nT) for every t in both x1(t) and x2(t) and then take the Fourier transform of that, cut of the edges where the transforms are equal to zero and then that is where I go blank...

I imagine that is the right implementation to start the problem with, but please correct me if I am wrong. Thank you in advance to all who may be able to help - it is much appreciated!!!
 

Answers and Replies

  • #2
vela
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Hint: convolution theorem.
 
  • #3
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I can see where convolution comes into play, but how can I implement the CTF transforms that are given?
 
  • #4
vela
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What sets the lower limit on the sampling rate if you want to be able to recover the original signal?
 
  • #5
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The Nyquist rate, to sample at the perfect rate (without aliasing/oversampling to occur) - it would be = 2fmax
 
  • #6
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I am pretty confused at what you're trying to hint at here. I appreciate the help, but my mind is still blank.
 
  • #7
vela
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It's kind of hard to say anything without giving away the answer. Think about Y(jω). Where is it zero? Can you deduce fmax from that information?
 

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