It is possible to find closed expressions for the DFT of simple sequences, particularly those involving "discrete" steps and ramps. Sinusoids can also be summed but the expressions tend to be quite long.

Here a simple sequence x(n) given by the following expression is considered.

For comparison the DTFT of the same sequence is shown below. T here is the sampling time.

The coefficient in the complex form of the definition of the Fourier Series of a function with period T and equal to 1 for 0 £ t £ t is shown below.

The Fourier Transform of a pulse f(t) = 1 for 0 £ t £ t is also shown below for comparison.

COPYRIGHT © 2007 Cuthbert Nyack.