LeCroy DDA 7 Zi series, Operator'S Manual

Page: 157 / 544

Operator's Manual
WP700Zi-OM-E-RevA
156
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 collects the signal energy that falls into the immediate
neighborhood of its center 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 RangeThe 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 is equal to the bin width Delta f. That is, if the input signal changes its
frequency by Delta f, the corresponding spectrum peak will be displaced by
D
f. For smaller changes of frequency, only the shape of the peak
will change.
However, the effective frequency resolution (that is, the ability to resolve two signals whose frequencies are 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
lists the ENBW values for the implemented windows.
Leakage In the power spectrum of a sine wave with an integral number of periods in the (rectangular) time
window (that is, the source frequency equals one of the bin frequencies), the spectrum contains a sharp
component whose value accurately reflects the source waveform's amplitude. For intermediate input frequencies
this spectral component has a lower and broader peak.
The broadening of the base of the peak, stretching out into many neighboring bins, is termed leakage . It is due to
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 available window functions is applied.
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 TheFFT is computed over the number of points (Transform Size) whose upper bounds are the
source number of points, and by the maximum number of points selected in the menu. The FFT generates
spectra of N/2 output points.
Nyquist Frequency The Nyquist frequency is equal to one half of the effective sampling frequency (after 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 3.92 dB lower (1.57 times) when the source frequency is halfway
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 the
Flattop window.
Power Spectrum The power spectrum (V
2
) is the square of the magnitude spectrum.
The power spectrum is displayed on the dBm scale, with 0 dBm corresponding to:
V
ref
2
= (0.316 V
peak
)
2
,
where V
ref
is the peak value of the sinusoidal voltage, which is equivalent to 1 mW into 50 ohms
.
Power Density Spectrum The power density spectrum (V
2
/Hz) is the power spectrum divided by the equivalent
noise bandwidth of the filter, in hertz. The power density spectrum is displayed on the dBm scale, with 0dBm
corresponding to ( V
ref
2
/Hz).
Sampling Frequency The time-domain records are acquired at sampling frequencies dependent on the selected time base. Before the FFT
computation, the time-domain record may be decimated. If the selected maximum number of points is lower than the source number of points,
the effective sampling frequency is reduced. The effective sampling frequency equals twice the Nyquist frequency.
Scallop Loss This is loss associated with the picket fence effect.
Window Functions All available window functions belong to the sum of cosines family with one to three non-zero cosine terms: