Is this a valid question? H(ω-ωo) + H(ω+ωo) = 2*H(ω)

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Discussion Overview

The discussion revolves around the validity of a question related to the amplitude response of a filter characterized by the equation H(ω-ωo) + H(ω+ωo) = 2*H(ω). Participants explore the implications of this equation and the potential for multiple interpretations based on the lack of context.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question whether the original question is valid without additional context, suggesting that multiple answers could exist.
  • One participant notes that if the equation holds for all ω, it allows for significant deductions about H(ω).
  • Another participant expresses that the original question was poorly framed, indicating that the amplitude response could take various forms, such as square or triangular shapes, due to the lack of details.
  • A participant proposes that if the equation is valid for all ω, then H(ω) could be expressed as H(ω)=cω+m+f(ω), where f(ω) is an arbitrary periodic function with period ωo.
  • Another participant speculates that the question asker intended for others to recognize that H(s) is periodic, implying that its frequency response resembles a comb filter.

Areas of Agreement / Disagreement

Participants express differing views on the validity and clarity of the original question, indicating that there is no consensus on whether it is well-framed or if it can be answered definitively without additional context.

Contextual Notes

The discussion highlights limitations related to the assumptions made about the equation and the definitions of terms involved, as well as the potential for ambiguity in interpreting the question.

wirefree
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Draw the amplitude response of a filter whose characteristic equation is:

H(ω-ωo) + H(ω+ωo) = 2*H(ω)
I thank you for reading this question.

If given as is, is this a valid question? I ask because, without context, I reckon there could be multiple answers to it.

Your terse response - a yes or no - is all that’s requested.wirefree
 
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If this equation is valid for all ω you can determine a lot about H(ω).
 
mfb said:
If this equation is valid for all ω you can determine a lot about H(ω).

Thank you, mfb.

I can appreciate your point of view. On a closer look, it's my question that wasn't framed well.
Please allow me another opportunity.

When asked to draw the amplitude response of a filter whose characteristic equation is given to be such and such, and that's all that's known and given, I meant, when I expressed the doubt that "there could be multiple answers", that the amplitude response could take any shape - square, triangular, etc.

I am sure you'll see now what I meant: the question lacks details.

Please do share a thought.
wirefree
 
What I was hinting towards: If H(ω-ωo) + H(ω+ωo) = 2*H(ω) for all ω then H(ω)=cω+m+f(ω) where f(ω) is an arbitrary periodic function with period ωo.
 

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