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Digital signal processing, linear time invariant system,

  1. Apr 27, 2014 #1
    I really confused, I found in a book that the following system,
    y[n]= x[n+1]-x[n], is not causal!
    But from the definition of causality that the output y[n0] depends only on the input samples x[n] for n<=n0,,,
    So I think that this system is causal...

    If you agree with me please tell me that it's correct...

    Thanks in advance...
  2. jcsd
  3. Apr 27, 2014 #2


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    x[n+1] is not a past or present sample of the input it is a future sample so that is why it is not causal.

    It's actually like this, x[n-k] where k>=0
  4. Apr 27, 2014 #3
    But x[n+1] means that the sample is shifted to the left, (less than 0 or means it is positioned at -1) so it is a past value then the system is causal.!!!!
  5. Apr 27, 2014 #4


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    It's true that x[n+1] would be x[n] shifted to the left by one, but x[n+1] is a future value. Think about the graphs - if we have x[n] = {1,2,3,4..} where 1 has the zero place, x[n+1] would be, as you say, {2,3,4,5..} with 2 having the zero place. Do you see how now the first sample in x[n+1] (which is 2) is the FUTURE value of x[n] at the ones place?

    You're right that the graph shifts, this is visual meaning of future values. The graph does shift left.
  6. Apr 28, 2014 #5

    Thanks for your answer... It is clear now.. Thanks
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