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where M
= 0.316 V (that is, 0 dBm is defined as a sine wave of 0.316 V peak or 0.224 V rms, giving 1.0 mW
ref
50 ohms).
The dBm Power Spectrum is the same as dBm Magnitude, as suggested in the above formula.
dBm Power Density:
ere ENBW is th
wh
e equivalent noise bandwidth of t
the current frequen
cy resolution (bin width).
rage takes the complex frequency-domain data R'
The FFT Power Ave
Step 5, and co
mput
es the square of the magnitude:
2
2
2
M
= R'
+ I'
,
n
n
n
then sums M
2 a
nd
counts the accumulated spectra. The total is normalized by the number of spectra and
n
converted to the
se
lected result type using the same formulas as are used for the Fourier Transform.
FFT Glossary
This section
defines
the terms freq
Aliasing If th
e inpu
t signal to a sampling acquisition system contains components whose frequency is greater
than the N
yquist fre
quency (half the sampling frequency
The result is that the
contribution of these components to the sampled waveform is indistinguisha
the Nyquist frequency. This is aliasing.
components below
Th
e timebase and transform size should be selected so that the resulting Nyquist frequency is higher than the
highest significant component in the time
Coherent Ga
in The norm
rectangula
r window and le
multiplication by the windo
the values for t
he implemented win
Window Type
Rectangular
von Hann
Hamming
Flat Top
Blackman-Harris
ENBW Equivalent Noise BandWidth (ENBW) is the bandwidth of a rectangular filter (same gain at the center
frequency), equivalent to a filter associated with each frequency bin, which would collect the same power from
white noise signal. In the table on the previous page, the ENBW is listed for each window function implemented,
given in bins.
Filters Computing an
N-point FFT is equivalent to passing the time-domain input signal through N/2 filters and
plotting their outputs against the frequency. The spacing of filters is Delta f = 1/T, while the bandwidth depends on
the window function used (see Frequency Bins).
Frequency Bins The FFT algorithm takes a discrete source waveform, defined over N points, and compute
complex Fourier coefficients, which are interpreted
WRXi-OM-E Rev C
uently used in FFT spectrum analysis and relates them to the oscilloscope.
-domain record.
alized cohe
rent gain of a filter co
ss than 1.0 for
other windows. It defines the loss of sig
w functio
n. This lo
ss is compensate
dows
.
Window Frequency Do
Highest Side Lobe
(dB)
-13
-32
-43
-44
-67
he filter corresponding to the sel
and I'
n
), there will be less than two samples per signal period.
rre
sponding to ea
d for in the oscilloscope. Th
main
Parameter
Scallop Loss
(dB)
3.92
1.42
1.78
0.01
1.13
as harmonic components of the input signal.
O
'
PERATOR
ected window, and Delta f is
for each spectrum generated in
n
ble from that of
ch win
dow fun
ction
is 1.0 (0 dB) for a
n
al energ
y due
to the
e following table lists
s
ENBW
Coherent Gain
(bins)
1.0
0.0
1.5
-6.02
1.37
-5.35
2.96
-11.05
1.71
-7.53
M
S
ANUAL
into
(dB)
a
s N
139
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