December 2014
Intermediate to advanced
768 pages
22h 47m
English
Content preview from Signal Processing for Cognitive Radios
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6.5.1 Temporally Windowed Observations
With the notation in (6.59), we see that TVFT-DTFT (6.62) is equivalent to the DTFT of the observation signal 
:
(6.67a)
(6.67b)
Hence, X(F, n;N) is the convolution of the spectral component x[n]e–j2πFn in x[n] with the rectangular function centered at time n = 0 with a finite width N. The final result is to smoothen, or broaden, the spectral component by an order of 
.
Then it is also possible to replace the rectangular window in (6.59) by a general data tapering function wN[n] that is nonzero only for 
. Let us denote by xw;n0 [n] the tapered data obtained by using a data taper WN[n]:
(6.68)
The resulting DTFT of the tapered data x[n]wN[n – n0] is
(6.69)
where last step follows by noting that wN[n] is an N-length taper centered at n = 0. ...
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