# Complex Fourier Spectrum

• JohnSimpson

#### JohnSimpson

I feel I have a good grasp of the complex Fourier series, but I'm struggling with a few things still.

When I take, say, an fft in MATLAB (with an even number of data points) I obtain a spectrum that looks like this

[DC] [ + freqs ] [Real Valued Number] [-Freqs]

With complex conjugate symmetry around the Real Value in the middle. I understand why this value in the middle cannot have an imaginary component, as it would destroy the symmetry. The value is it's own complex conjugate. But what is this value? Is it the maximum frequency in the spectrum?

In a related question, say I want to integrate in the frequency domain. That would involve diving by the entire signal by $$2pif_nj$$ where fn is the fundamental frequency times n. How do I then deal with the DC value, and the real value in the middle? It seems to me that for the DC value I would be diving by zero, and for the real value in the middle of the spectrum, I would be making it complex. Corrections to my understanding are appreciated

-John

bump!