Digital signal processing, linear time invariant system,

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Discussion Overview

The discussion revolves around the causality of a digital signal processing system defined by the equation y[n] = x[n+1] - x[n]. Participants explore the implications of the system's definition on its causal nature, examining the relationship between input and output samples.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant argues that the system is causal based on the definition that the output y[n0] depends only on input samples x[n] for n <= n0.
  • Another participant counters that x[n+1] represents a future sample, thus making the system non-causal.
  • A different viewpoint suggests that x[n+1] can be interpreted as a past value due to its position in the equation, arguing for causality.
  • Further clarification is provided that while x[n+1] shifts the graph left, it still represents a future value of the input, reinforcing the non-causal argument.

Areas of Agreement / Disagreement

Participants express conflicting views on the causality of the system, with no consensus reached. Some argue for causality based on definitions, while others maintain that the presence of future samples indicates non-causality.

Contextual Notes

The discussion highlights the ambiguity in interpreting the relationship between input and output samples, particularly regarding the definitions of past, present, and future values in the context of digital signal processing.

Asma
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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...
 
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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
 
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.!
 
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.
 
FOIWATER said:
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.
Thanks for your answer... It is clear now.. Thanks
 

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