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W
R
X
S
AVE
UNNER
I
For a real source waveform (imaginary part equals 0), there are only N/2 independent harmonic components
An FFT corresponds to analyzing the input signal with a bank of N/2 filters, all having the same shape and width,
and centered at N/2 discrete frequencies. Each filter
neighborhood of its ce
nter frequency. Thus it can be said that there are N/2 "frequency bins."
The distance in hertz between the center frequencies of two neighboring bins is always:
Delta f = 1/T
where T is the duration of the time-domain record in seconds.
The width of the main lobe of the filter centered at each bin depends on the window function used. The
rectangular window has a nominal width at 1.0 bin. Other windows have wider main lobes (see table).
Frequency Range The range of frequencies computed and displayed is 0 Hz (displayed at the left-hand edge of
the screen) to the Nyquist frequency (at the rightmost edge of the trace).
Frequency Resolution In a simple sense, the frequency resolution
input signal changes its frequency by Delta f, the corresponding spe
smaller cha
nges of frequency, only the shape of the peak will change.
However, the effective frequency resolution (that is, the ability to resolve two signals whose frequenc
almost the same) is further limited by the use of window functions. The ENBW value of all windows other than the
rectangular is greater than Delta f and the bin width. The table of Window Frequency-Domain Parameters li
ENBW values for the implemente
Leakage In the power spectrum of a sine wave with an integral number
window (that is, the sou
componen
t whose value accurately reflects the source waveform's amplitude. For intermediate input frequencies
this spectral component has a lower and broad
ening of the base of the peak, stretching out into many neighboring bins, is termed leakage. It is due to
The broad
the relatively high side lobes of the filter associated with each frequency bin.
The filter side lobes and the resulting leakage are reduced when one of the
The best reduction is provided by the Blackman-Harris and Flattop windows. However, this reduction is offset by a
broadening of the main lobe of the filter.
Number of Points The FF
the source number of po
spectra of N/2 output p
oints.
Nyquist Frequency The Nyquist frequency is equal to one half of the
decimation): Delta f x N/2.
Picket Fence Effect If a sine wave has a whole number of periods in the time domain record, the power
spectrum obtained with a rectangular window will have a sharp peak, corresponding exactly to the frequency and
amplitude of the sine wave. Otherwise the spectrum peak with a rectangular window will be lower and broader.
The highest point in the power spectrum can be 3.9
between two discrete bin frequencies. This variation of the spectrum magnitude is called the picket fence effect
(the loss is called the scallop loss).
All window functions compensate for this loss to some extent, but the best compensation is obtained with th
Flattop window.
Power Spectrum The power spectrum (V
The power spectrum is displayed on the dBm scal
2
2
V
= (0.316 V
)
,
ref
peak
where V
is the peak value of the sinusoidal voltage, which is equivalent to 1 mW into 50 ohms.
ref
140
ERIES
d windows.
rce frequency equals one of the bin frequencies), the spectrum contains a sharp
er peak.
T is computed over the number of points (Transform Size) whose upper bounds are
ints, and by the maximum number of points selected in the menu. The FFT generates
2
) is the square of the magnitude spect
collects the signal energy that falls into the immediate
is equal to th
ctrum peak w
of periods in the (rectangular) time
effective sampling frequency (after the
2 dB lower (1.57 times) when the source frequency is halfway
e, with 0 dBm corresponding to:
e bin width Delta f. That is, if the
ill be displaced by Df. For
available window functions is applied.
rum.
.
ies are
sts the
e
WRXi-OM-E Rev C
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