For the DFT, all signals and spectra are length . A length sequence can be denoted by , , where may be real () or complex (). We now wish to regard as avector 6.1 in an dimensional vector space. That is, each sample is regarded as a coordinate in that space. A vector is mathematically a single point in -space represented by a list of coordinates called an -tuple. (The notation means the same thing as .) It can be interpreted geometrically as an arrow in -space from the origin to the point .
We define the following as equivalent:
where is the th sample of the signal (vector) . From now on, unless specifically mentioned otherwise, all signals are length .