How to Correctly Convolve x[n] with a Unit Step Function?

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Discussion Overview

The discussion revolves around the convolution of a discrete-time signal x[n] with a unit step function h[n] = u[n]. Participants explore different methods for performing the convolution, including graphical and analytical approaches, while seeking clarification on the correctness of their methods.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant describes their approach using a graphical method, flipping and shifting h[n] but obtaining all zeros, questioning the correctness of this method.
  • Another participant suggests using the definition of convolution, providing a formula and indicating that they arrive at a non-zero sequence of numbers, implying a different outcome from the first participant's method.
  • A third participant shares a link to a demonstration of the graphical approach, suggesting it may help clarify the process.
  • Another participant proposes viewing x[n] as a sum of shifted and scaled impulses, indicating that the convolution with a shifted impulse results in a shifted version of h[n], which should then be summed.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correctness of the graphical method versus the analytical approach, with multiple competing views on how to properly perform the convolution.

Contextual Notes

Some participants' methods depend on assumptions about the properties of the signals involved, and there may be missing details regarding the specific form of x[n] and its relationship to the unit step function.

redundant6939
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Homework Statement


Find convolution of x[n] (graph in attachment) and h[n] where h[n] = u[n]
Capture.PNG

Homework Equations

The Attempt at a Solution


- flipped the h[n] to have h[-n]
- moved to the left once (h[-1-n]) to align
- multiplied h and x and it gives me all zeros

Is this correct or I'm missing something?
 
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I don't know about your graphical algorithm but if you use the definition

y[n] = x[n]*h[n] = ∑ (k = -∞ to +∞) x[k] h[n-k]

then I get a non-zero sequence of numbers:

a+0.5, b+0.5, c+0.5, c+0.5, d+0.5, d+0.5, d+ 0.5, ...

wher a, b , c, and d are positive integers for you to find.
 
Just think x(n) as sum of shifted and scaled impulses . Since you know the convolution of a signal h(n) with shifted impulse will be shifted h(n) and then you add them .
 

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