Discrete Fourier Transform: What is the DC Term really? I am currently toying around with the Discrete Fourier Transform (DFT) in Matlab to extract features from images. I like to fully understand the concepts that I use. I have read several explanations, such as this, but so far, none really explained the meaning of the "DC term". All I know is that the k'the term of the DFT can be written as: 






where 
 is the twiddle factor.

That means that the first term (the DC term), , is an amplitude without frequency.

Can someone explain why is it called the DC term? What is it's relation to "Direct Current"? And what is the relevance of the DC term? When is it useful, and for what?
The DC term is the 0 Hz term and is equivalent to the average of all the samples in the window (hence it's always purely real for a real signal). The terminology does indeed come from AC/DC electricity - all the non-zero bins correspond to non-zero frequencies, i.e. "AC components" in an electrical context, whereas the zero bin corresponds to a fixed value, the mean of the signal, or "DC component" in electrical terms.

As far as practical applications go, the DC or 0 Hz term is not particularly useful. In many cases it will be close to zero, as most signal processing applications will tend to filter out any DC component at the analogue level. In cases where you might be interested it can be calculated directly as an average in the usual way, without resorting to a DFT/FFT.