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**coherence** estimates the
coherence and cross-spectrum of a pair of real-valued time series; as a
byproduct of its calculation of coherence, it also estimates the autospectra
of each of its input time series. The *file* argument specifies the name
of a text file containing the samples of the series in two columns. The
standard output contains five columns of numbers (optionally preceded by
column headings), which are frequency (Hz), coherence, cross-spectral power
(dB), autospectral power (dB) of the first time series, and autospectral
power (dB) of the second time series.

This program is based on a Fortran
program by C.R. Arnold, G.C. Carter, and J.F. Ferrie, as described in ‘A coherence
and cross-spectral estimation program’, by G.C. Carter and J.F. Ferrie, in *Programs
for Digital Signal Processing*, edited by the Digital Signal Processing
Committee of the IEEE ASSP Society (New York: IEEE Press, 1979). The functions
fft842() and its auxiliary functions r2tx(), r4tx(), and r8tx(), are based
on Fortran subroutines by G.D. Bergland and M.T. Dolan, as described by them
in ‘Fast Fourier transform algorithms’, also included in *Programs for Digital
Signal Processing*.

*Options* are:

**-f***frequency*- Specify the sampling frequency in Hz (default: 250).
**-n***n*- Process the input in overlapping chunks of
*n*samples (default: 1024). For best results,*n*should be a power of two. **-v**- Print column headings.
**-x***sx sy*- Specify multiplicative scale factors for the two time series (defaults: 1). A reasonable choice is to use the reciprocals of the standard deviations of the respective time series if these differ significantly.

Note that the scale factors generally have little or no visible effect
on the coherence or on the shape of the spectra. The choice of chunk size
(using the **-n** option) will have a significant effect; some experimentation
may be needed to determine an appropriate chunk size in each case.

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Updated 28 May 2015