Lambda SR1, Operation Manual, Page: 143 / 317

SR1 Operation 143
© 2014 Stanford Research Systems
phase relative to the beginning of the time record for each averaged FFT. Below, the averaged Linear
Spectrum (Navg=100) is shown plotted with the averaged Power Spectrum for the same number of
averages. Note that averaging the linear spectrum does not reduce the variation in the noise floor, but
does reduce the amount of noise. In this case averaging 100 spectra has reduced the noise floor by
about 20 dB.
Com parison of Averaged Pow er Spectrum and Linear Spectrum
Computing the 2-Channel Frequency Response
After computing the Power Spectrum and Linear Spectrum for both channels, DSP computes the
Frequency Response. The complex frequency response is defined in terms of the FFTs for the two
channels as:
is a mathematically "volatile" expression because it diverges when the A-channel input is small. To
minimize this volatility SR1 uses a standard technique called the "Tri-Spectral Average" when computing
the dual-channel frequency response. If we multiply the numerator and denominator of the equation
above by the complex conjugate of the A-channel FFT and average the numerator and denominator
separately we get the following expression for the averaged frequency response:
The denominator of this expression is simply the Power spectrum of the input channel, which is by
definition a positive, real quantity. The numerator, , is a complex quantity known as
the cross-spectrum. When SR1 calculates the magnitude and phase of the frequency response it uses
the following definitions:
This technique provides a significantly more stable Frequency Response than if SR1 were to simply
average the shot by shot frequency response .
Coherence
The FFT2 analyzer also calculates another 2-channel scalar measurement, the coherence. Coherence is
measure of the fraction of the output power at a frequency that is phase coherent with the input. A