O
PERATOR
’
S
M
ANUAL
WRXi-OM-E Rev B
139
where
M
ref
= 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 into
50 ohms).
The dBm Power Spectrum is the same as dBm Magnitude, as suggested in the above formula.
dBm Power Density:
where
ENBW
is the equivalent noise bandwidth of the filter corresponding to the selected window, and
Delta f
is
the current frequency resolution (bin width).
The FFT Power Average takes the complex frequency-domain data
R'
n
and
I'
n
for each spectrum generated in
Step 5, and computes the square of the magnitude:
M
n
2
= R'
n
2
+ I'
n
2
,
then sums
M
n
2
and counts the accumulated spectra. The total is normalized by the number of spectra and
converted to the selected result type using the same formulas as are used for the Fourier Transform.
FFT Glossary
This section defines the terms frequently used in FFT spectrum analysis and relates them to the oscilloscope.
Aliasing
If the input signal to a sampling acquisition system contains components whose frequency is greater
than the Nyquist frequency (half the sampling frequency), there will be less than two samples per signal period.
The result is that the contribution of these components to the sampled waveform is indistinguishable from that of
components below the Nyquist frequency. This is
aliasing
.
The timebase and transform size should be selected so that the resulting Nyquist frequency is higher than the
highest significant component in the time-domain record.
Coherent Gain
The normalized coherent gain of a filter corresponding to each window function is 1.0 (0 dB) for a
rectangular window and less than 1.0 for other windows. It defines the loss of signal energy due to the
multiplication by the window function. This loss is compensated for in the oscilloscope. The following table lists
the values for the implemented windows.
Window Frequency Domain Parameters
Window Type
Highest Side Lobe
(dB)
Scallop Loss
(dB)
ENBW
(bins)
Coherent Gain
(dB)
Rectangular
-13 3.92
1.0
0.0
von Hann
-32 1.42
1.5
-6.02
Hamming
-43 1.78
1.37
-5.35
Flat Top
-44 0.01
2.96
-11.05
Blackman-Harris
-67 1.13
1.71
-7.53
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 a
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 computes N
complex Fourier coefficients, which are interpreted as harmonic components of the input signal.
