The Discrete Fourier Transform (DFT) of a signal may be defined by
where ` ' means ``is defined as'' or ``equals by definition'', and
The sampling interval is also called the sampling period. For a tutorial on sampling continuous-time signals to obtain non-aliased discrete-time signals, see Appendix D.
When all signal samples are real, we say . If they may be complex, we write . Finally, means is any integer.