Lambda SR1, Operation Manual, Page: 142 / 317

SR1 Operation Manual 142
© 2014 Stanford Research Systems
stage of decimation includes filtering to eliminate alias effects from the discarded portions of the
frequency spectrum. The outputs are sent to two buffers which serves as the time records for the FFT2
analyzer. The time records for each channel are synchronized to the occurrence of a trigger. If the
analyzer trigger is not enabled then a trigger is automatically generated as soon as the DSP has
finished processing the previous time record. Otherwise, the analyzer waits for a trigger which matches
the specified
trigger criteria and begins both time records at the trigger point.
After a trigger occurs and enough time record points have been accumulated to compute a spectrum of
the specified resolution, the DSP applies a windowing function to the time-domain data (See
Window
Selection ). Windowing is necessary due to the finite length of the FFT time record. Unless the input
signal happens to be periodic in the time record, discontinuities at the beginning and end of the time
record will appear as significant broadening of the true spectrum of the input signal. Typical window
functions are large in the middle of the time record and taper off at the beginning and ends, thus
minimizing the discontinuities.
After windowing, the DSP computes the FFT of the windowed time records. For a resolution of N lines,
2N real time record points are used to compute an FFT of N complex points. Each FFT is then averaged
in two different ways. The
Power Spectrum is computed by computing the power for each spectrum
(taking the absolute value of the complex FFT points) and averaging that power into the power computed
for previous FFTs. This type of averaging does not reduce the noise floor of the spectrum but it does
reduce the variation of the noise floor making it easier to see spectral details on the order of the noise
amplitude. Phase information is lost when computing the Power Spectrum. In the example below the
unaveraged power spectrum is shown for a signal composed of a 1 kHz sine wave with added white
noise. The second spectrum shows averaging on and Navg = 10. Note the substantial reduction in the
variation of the noise floor and note also that the average value of the noise floor is the same.
Unaveraged Pow er Spectrum of Sine+Noise
Averaged (N=10) Pow er Spectrum of Sine+Noise
The second spectral output computed by the FFT2 analyzer is the Linear Spectrum for each channel.
The Linear Spectrum is computed by averaging the real and imaginary parts of each FFT separately. The
average of the real and imaginary parts are then used to compute the Linear Spectrum amplitude and
phase. In the Linear Spectrum, unlike the Power Spectrum, noise that is uncorrelated to the signal is
actually reduced by further averaging. Because of this, use of the Linear Spectrum, unlike the Power
Spectrum, requires that the time record be triggered so that the signal waveform will have the same