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Then the Fourier transform of signal is given by: |
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If we now evaluate the above integral by trapezoidal rule of integration after padding two zeros (red dots in fig 33.1) at the extremity on either side [where the signal is zero], we obtain the following expressions. |
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The corresponding inverse which is used to reconstruct the signal is given by:
|
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If from equation (1) we could compute complete frequency spectrum i.e.  then (2) would imply that we can obtain  . The fallacy in the above statement is quite obvious as we have only finite samples and the curve connecting any 2-samples can be defined plausibly in infinitely many ways (see fig 33.2). This suggests that from (1), we should be able to derive only limited amount of frequency domain information. |
of duration 
sampled at (fig 33.1) a uniform rate 
such that 
where 
is an integer 
.
