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I have a set of samples that represents a waveform. This waveform resembles a frequency modulated sinusoidal wave (only it is not).

I would like to invert this waveform or shift it by $2\pi$ shift it by $\pi$. of course taking the cosine of samples as they are without preprocessing is wrong.

What should I do to achieve this?

Thank you.

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Shifting by 2π is the same as doing nothing. I guess it's not what you want. Can you clarify the question ? – Frédéric Grosshans Nov 23 '10 at 13:08
you are right, it wouldn't do a thing! what I would like to get is a mirror reflection of the waveform over the x-axis but with the same dc-component as the original waveform (I don't want to shift it on the Y-axis). – mbadawi23 Nov 23 '10 at 13:26
Do you mean you have a Fourier spectrum of the waveform? – ptomato Nov 23 '10 at 13:31
I think my problem that I was shifting by $2\pi% instead of just pi, Dah! And thanks Frédéric Grosshans. I'll share my answer with you guys. – mbadawi23 Nov 23 '10 at 13:36
What does this have to do with physics? – endolith Nov 24 '10 at 1:08

Based on what you write in the comments, perhaps you can just calculate the DC component by taking the average, subtract that, flip it over the X axis, and add the DC component back.

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Yes, but how exactly do you suggest to flip it over the x-axis? – mbadawi23 Nov 23 '10 at 15:37
Multiply by -1? – mtrencseni Nov 23 '10 at 17:22
@mbadawi23 : another way to apply @mtrencseni solution. Compute the average $a$, and replace each sample $s_i$ by $2a - s_i$ – Frédéric Grosshans Nov 26 '10 at 15:42
  • For each sample I calculated the angle $\theta = i * 2\pi$
  • Then I added $\pi$ to $\theta$ while calculating sine and cosine components.
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This solution is way more complex than @mtrencseni 's solution, at least for an angla as simple than $\pi$ – Frédéric Grosshans Nov 26 '10 at 15:44

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