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I'm having some issues understanding something about the Fourier transform. In my first signals and systems class we used the angular frequency omega. Doing it like that you end up with a weighing factor or 1/(2pi) when you take the transform. Now in the dsp class I am taking now we are using the frequency in Hz.

The thing I don't get is how can the amplitude in one frequency be different than in another for the same signal. I also read about another way of doing it where in both directions you multiply it by 1/sqrt(2pi), helping to preserve duality.

Is the frequency transform basically different based on how it is interpreted? Can someone help me out here, I don't know exactly what I am confused about but I don't see how it can just be arbitrarily defined and have different amplitudes for what is apparently the same thing just in a different frequency?

For example a sine wave has an amplitude of 1. So it would seem reasonable that in the Fourier transform it would have an impulse of 1 at the correct frequency. But if you use radians for the Fourier transform, it has a different amplitude!

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# Homework Help: Need help understanding Fourier transform in Hz vs radians

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