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

## Main Question or Discussion Point

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.

Best,
wirefree

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mfb
Mentor
If this equation is valid for all ω you can determine a lot about H(ω).

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.

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.

Best,
wirefree

mfb
Mentor
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.

eq1
Gold Member