Someone please explain negative frequencies in the Fourier transform? I read all possible explanations including the formula for the cosine derived from the Euler's identity, but still don't get it.
And explanations like this drive me nuts: https://dsp.stackexchange.com/questions/431/what-is-the-physical-significance-of-negative-frequencies
I get the mathematical slight of hand but what does that have to do with actual real signals?
One of the explanations I've read:
>from the point of the Fourier transform, a real sinusoid is "really" the sum of two complex sinusoids spinning in opposite directions.
Why is that? I can't see that in the definition of the Fourier transform or the series (the integral). It doesn't even have to be complex. The fourier series could be thought of as a sum of cosines with different magnitudes and phases. You can write it down in a complex form as a shorthand, but how does that explain negative frequencies?
And explanations like this drive me nuts: https://dsp.stackexchange.com/questions/431/what-is-the-physical-significance-of-negative-frequencies
I get the mathematical slight of hand but what does that have to do with actual real signals?
One of the explanations I've read:
>from the point of the Fourier transform, a real sinusoid is "really" the sum of two complex sinusoids spinning in opposite directions.
Why is that? I can't see that in the definition of the Fourier transform or the series (the integral). It doesn't even have to be complex. The fourier series could be thought of as a sum of cosines with different magnitudes and phases. You can write it down in a complex form as a shorthand, but how does that explain negative frequencies?
