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W
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UNNER
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Power (Density) Spectrum
Because of the linear scale used to show magnitudes, lower amplitude compon
components. In addition to the functions offering magnitude and phase representations, the FFT option offers
power density and power spectrum density functions. These latter functions are even better suited for
characterizing spectra. The power spectrum (V
voltage equivalent to 1 mW into 50 ohms.) Thi
peaks — periodic signals, for instance.
The power density spectrum (V
associated with the FFT calculation.
Memory for FFT
The amount of acquisition memory available will determine the maximum range (Nyquist frequency) over which
signal components can be observed. Consider the problem of determining the length of the observation window
and the size of the acquisition buffer if a Nyquist rate of 500 MHz and a resolution of 10 kHz are required. To
obtain a resolution of 10 kHz, the acquisition time must be at least:
T = 1/Delta f = 1/10 kHz = 100 ms
For a digital oscilloscope with a memory of 100 kB, the highest frequency that can be analyzed is:
Delta f x N/2 = 10 kHz x 100 kB/2 = 500 MHz
FFT Pitfalls to Avoid
Take care to ensure that signals are correctly acquired: improper waveform positioning within the observation
window produces a distorted spectrum. The most common distortions can be traced to insufficient sampling, edge
discontinuities, window
ing or the "picket fence" effect.
Because the FFT acts like a bank of band-pass filters centered at multiples of the frequency resolution,
components that are not exact multiples of that frequency will fall within two consecutive filters. This results in an
attenuation of the true amplitude of these components.
Picket Fence and Scallop
The highest point in the spectrum can be 3.92 dB lower when the source frequency is half
discrete frequencies. This variation in spectrum magnitude is the picket fence effect. T
attenuation loss is referre
ensuring that the magnitu
If a signal contains a frequency component above Nyquist, the spectrum will be aliased, meaning that the
frequencies will be folded back and spurious. Spotting aliased frequencies is often difficult, as the aliases may
ride on top of real harmonics. A simple way of checking is to modify the sample rate and observe whether the
frequency distribution changes.
Leakage
FFT assumes that th
e signal contained within the time grid is replicated endlessly outside the observation
window. Therefore if the signal contains discontinuities at its edges, pseudo-frequencies will appear in the
spectral domain, distorting the r
frequ
ency falls within two frequency cells, broadening the spectrum.
The broadening of the base, stretching out in many neighboring bins, is termed leakage. Cures for this are to
ensure that an integral number of periods is contained within the display grid or that no discontinuities appear at
the edges. Another is to use a window function to smooth the edges of the signal.
Choosing a Window
The choice of a spectral window is dictated by the signal's characteristics. Weighting functions control the filter
response shape, and affect noise bandwidth as well as side lobe levels. Ideally, the main lobe should be as
narrow and flat as possible to effectively discriminate all spectral components, while all side lobes should be
136
ERIES
2
) is the
s is the representation of choice for signals containing isolated
2
/Hz) is the power spectrum divided by the equivalent noi
This is best employed for characterizing broadband signals such as noise.
d to as scallop loss. LeCroy oscilloscopes automatically correct for the scallop effect,
de of the spectra lines correspond to their true values in the time domain.
eal spectrum. When the start and end phase of the signal differ, the signal
square of the magnitude spectrum (0 dBm corresponds to
ents are often hidden by larger
se bandwidth of the filter
way between two
he corresponding
WRXi-OM-E Rev C
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