The discrete-time Fourier series, abbreviated DTFS, represents a periodic sequence. If 
,
its Fourier coefficients are
 |
where 
.
The inverse series is
 |
Thus one period of the sequence and one period of its coefficients form a discrete Fourier transform pair, with the normalization placed in the forward formula above. The DTFS applies to periodic discrete-time sequences, whereas the discrete-time Fourier transform applies to sequences that need not be periodic.
