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SR1 Operation Manual 144
© 2014 Stanford Research Systems
coherence value of "1" means all of the output is phase coherent with the input, while a value of "0"
indicates the output is completely uncorrelated with the input. Because only averaging over several FFTs
reveals which portions of the spectrum are phase coherent and which are not, the coherence
measurement is valid only when averaging.
Mathematically, the coherence is defined as
As an example consider the spectra below showing the frequency response and coherence of an 8-pole
6-zero elliptical filter with a 5 kHz passband frequency. The spectra were taken with the FFT2 analyzer
with the hi-bandwidth ADC, and a 1 Vrms synchronous chirp source outputting equal power into each
FFT bin up to 200 kHz. Note that throughout the passband of the filter and into the transition region the
coherence is unity. In the stopband however, the output signal is >80 dB below the input and at those
small levels there exists enough uncorrelated output noise in the filter output to reduce the coherence to
a value below one. At the zeros of the filter, there is virtually no output from the filter and all the SR1 is
measuring is uncorrelated noise, hence the zeros of the filter correspond to the regions of lowest
coherence.
Frequency Response and Coherence of Elliptical Filter
Impulse Response
SR1 computes the impulse response by taking the inverse FFT of the complex (magnitude and phase)
frequency response. Only portions of the frequency response which exceed the coherence threshold
(See
Coherence ) are used when computing the impulse response. Traditionally impulse response
measurements have been associated with the use of Maximum Length Sequences as a stimulus. The
MLS waveform has several useful properties which simplify the calculation of the impulse response and
has a crest factor close to 1 providing good signal to noise. However, because SR1 uses a full dual-
channel FFT to calculate impulse response it is not necessary to use MLS waveforms as a stimulus, in
fact most broadband sources will work. In particular, noise, MLS, FFT chirp, and log-sine chirp, are all
suitable waveforms for impulse response measurements.
Random noise is not a particularly good choice
and has a relatively poor crest factor, but is interesting for comparison purposes. The MLS waveform has
a good crest factor and sounds much like random noise, but can produce misleading results in systems
with transfer-function nonlinearities. The
FFT chirp waveform has a comparable crest factor to MLS and
has the additional advantage of being able to completely tailor the frequency content of the chirp to suit
the device under test. (The FFT chirp, however, does sound decidedly "non-random.") Finally, the
log-