DFT, Calculating Transform for Simple Signals.
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
The DFT can be obtained from the definition:-
This expression is readily summed resulting in the
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
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COPYRIGHT © 2007 Cuthbert Nyack.