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It can be considered that the energy of the signal at some frequency
n is distributed 50/50 between the first half and the second half of
the spectrum; the energy at frequency 0 is completely contained in
the 0 term.
(6) The sixth step is the elimination
of
results. Only the first half of the
Nyquist frequency is kept:
the redundant
part of the
spectrum (Re, Im), 0 to the
R' = 2 * ~n
0 < n < N/2
I 'n = 2 *
0 < n < N/2
n
n
-
(7) The seventh and last step is the computation of the waveform to be
displayed.
If you select the Real Part or Imaginary
Part Display
Type, no
further computation is done: the displayed waveform is R' or I' as
defined above.
If you select Magnitude mode, the magnitude is computed as:
!
M = | R '2 + I
'2
n~
n
n
In practice,
the steps described
above
lead to the following
result:
An AC sine wave of amplitude 1.0 V and an integral number
of periods
in the time window,
transformed
with the
rectangular window, results in a fundamental peak of 1.0 V
magnitude in the spectrum.
However, a DC component
of 1.0 V, transformed
with the
rectangular window, results in a fundamental peak of 2.0 V
magnitude in the spectrum.
The displayed waveforms for the other available modes are computed
as follows:
Phase: angle = arctan (In/Rn)
~n > M .
angle = 0
< Mm~
n
n - mln
where M
is the minimal magnitude, fixed at about 10 -3 of the full
scale ~e. 64 units on the scale of 65536, 16 bits), at any gain
setting.
11-14
Fast Fourier Waveform Processing
Option (WP02, V 2.06FT)
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