Stanford Research Systems SR785, Руководство по эксплуатации и программированию

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2-12 FFT Windowing
SR785 Dynamic Signal Analyzer
FFT Windowing
A signal which is not exactly periodic within the time record does not fall on an exact
frequency bin of the FFT spectrum (integer multiple of the FFT frequency resolution). Its
energy is split across multiple adjacent frequency bins. This is true but it's actually worse
than that. An FFT spectrum models the time domain as if a time record repeated itself
forever. This means the end of the time record is followed by the start of the time record
in a circular fashion. If the data is not continuous across the stop to start boundary, the
FFT will actually compute the spectrum of the discontinuity and ‘leak’ energy into all
frequencies in the spectrum.
Windows are functions defined over a time record which are periodic in a circular time
record. They generally start and end smoothly at zero and are smooth functions in
between. When the time record is windowed, its data samples are multiplied by the
window function, time point by time point, and the resulting windowed time record is
definitely periodic in the circular sense. Windowing eliminates the leakage in the
spectrum from signals not exactly periodic with the time record.
In The Frequency Domain
In the frequency domain, a window acts like a filter. The amplitude of each frequency
bin is determined by centering this filter on each bin and measuring how much of the
signal falls within the filter.
If the filter is narrow, then only frequencies near the exact bin frequency will contribute
to the bin. A narrow filter is called a selective window - it selects a small range of
frequencies around each bin. However, since the filter is narrow, frequencies slightly off
bin are attenuated and phase shifted. Selective windows are useful for resolving adjacent
peaks or improving signal to noise. They should not be used for accurate amplitude
measurements (except for signals at exact bin frequencies).
If the filter is wide, then frequencies farther from each exact bin will contribute to the bin
amplitude making the signal peaks very wide. However, off bin frequencies are not
attenuated. These windows should be used for accurate amplitude measurements rather
than good frequency resolution.
Windowing allows the FFT to accurately measure signals at frequencies which are not
exact frequency bins. The different types of windows trade off selectivity, amplitude
accuracy, and noise floor.
The SR785 offers many types of window functions - Uniform (no windowing), Flattop,
Hanning, Blackman-Harris (BMH), Kaiser, Force-Exponential, and User Defined
windows.
Uniform
The Uniform window is actually no window at all. The entire time record is used with
equal weighting. A signal will appear in a single frequency bin in the spectrum if its
frequency is exactly equal to a frequency bin. (It is exactly periodic within the time
record). If its frequency is between bins, it will leak into every bin of the spectrum.
These two cases also have a great deal of amplitude variation between them (up to 4 dB).