LeCroy 6000 SERIES, Operator'S Manual

Page: 213 / 409

WR6K-OM-E Rev A ISSUED: October 2003
211
Number of Points The FFT 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 0 dBm 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:
where: M = 3 is the maximum number of terms, a
m
are the coefficients of the terms, N is the
number of points of the decimated source waveform, and k is the time index.