The convolution of two functions with different parameters

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Discussion Overview

The discussion revolves around the linear convolution of a continuous signal with a Dirac delta function that has been shifted by a constant parameter. Participants explore the implications of using different variables in the convolution operation.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that the convolution of any function with the Dirac delta function results in the function itself, suggesting that the output will be the signal shifted by the parameter tau_p.
  • Another participant questions the validity of this assertion by pointing out that the Dirac delta function is defined in terms of tau, while the signal s(t) is defined in terms of t, raising concerns about the implications of this variable difference.
  • A third participant expresses uncertainty about the notation, suggesting that the use of tau in the Dirac delta function may be a typo, but acknowledges that unfamiliarity with a concept does not negate its validity in some contexts.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of using different variables in the convolution operation, and the discussion remains unresolved regarding the correctness of the initial assertion and the interpretation of the variables involved.

Contextual Notes

There is a lack of clarity regarding the notation used in the convolution operation, particularly the roles of tau and t, which may affect the interpretation of the convolution result.

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Hello all,

What is the result of this (linear) convolution:

[tex]s(t)\star\delta(\tau-\tau_p)[/tex]

where s(t) is a continuous signal, δ is the Dirac delta function, and \tau_p is a constant.

Thanks in advance
 
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Anything convoluted with the Dirac is its self. So give that you've shifted the dirace by tau the result would be s shifted by tau as well
 
cpscdave said:
Anything convoluted with the Dirac is its self. So give that you've shifted the dirace by tau the result would be s shifted by tau as well

You mean shifted by tau_p, right? But here the Dirac is a function of tau shifted by tau_p while s(t) is a function of t! Does this matter?
 
Hmmmm I did't notice that the dirac was using tau... I would think that is a typo in the question as it doesn't make sense. However to be fair just cause I haven't seen soemthing doesn't mean it doesn't make sense in some context...

With convolution the only time I've seen tau used as a varible is with the integral definition of the convolution operation...

Sorry I guess I should've read the question more carefully :(
 

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