Magnitude squared coherence
Cxy = mscohere(x,y)
Cxy = mscohere(x,y,window)
Cxy = mscohere(x,y,window,noverlap)
[Cxy,W] = mscohere(x,y,window,noverlap,nfft)
[Cxy,F] = mscohere(x,y,window,noverlap,nfft,fs)
[Cxy,F] = mscohere(x,y,window,noverlap,f,fs)
[...] = mscohere(x,y,...,'twosided')
Cxy = mscohere(x,y) finds
the magnitude squared coherence estimate,
of the input signals,
using Welch's averaged modified periodogram method.
The input signals may be either vectors or two-dimensional matrices.
If both are vectors, they must have the same length. If both are matrices,
they must have the same size, and
Cxy(:,n) = mscohere(x(:,n),y(:,n)).
If one is a matrix and the other is a vector, then the vector is converted
to a column vector and internally expanded so both inputs have the
same number of columns.
a one-sided coherence estimate. For complex
it returns a two-sided estimate.
mscohere uses the following default values:
FFT length which determines the frequencies at which the coherence is estimated
Maximum of 256 or the next power of 2 greater than the
length of each section of
Windowing function and number of samples to use for each section
Periodic Hamming window of sufficient length to obtain
eight equal sections of x and
Number of samples by which the sections overlap
Value to obtain 50% overlap
You can use the empty matrix,
Cxy = mscohere(x,y,window) specifies
a windowing function, divides
equal overlapping sections of the specified window length, and windows
each section using the specified window function. If you supply a
a Hamming window of that length.
Cxy = mscohere(x,y,window,noverlap) overlaps
the sections of
be an integer smaller than the length of
[Cxy,W] = mscohere(x,y,window,noverlap,nfft) uses
the specified FFT length
nfft to calculate the
coherence estimate. It also returns
W, which is
the vector of normalized frequencies (in rad/sample) at which the
coherence is estimated. For real
nfft/2 + 1)
nfft is even; if
odd, the length is (
nfft + 1)/2. For complex
the length of
real signals, the range of
W is [0, π]
nfft is even and [0, π)
nfft is odd. For complex signals, the range
W is [0, 2π).
[Cxy,F] = mscohere(x,y,window,noverlap,nfft,fs) returns
a function of frequency and a vector
F of frequencies
at which the coherence is estimated.
fs is the
sampling frequency in Hz. For real signals, the range of
even and [0,
odd. For complex signals, the range of
F is [0,
[Cxy,F] = mscohere(x,y,window,noverlap,f,fs) computes
the coherence estimate at the frequencies
a vector containing two or more elements.
[...] = mscohere(x,y,...,'twosided') returns
a coherence estimate with frequencies that range over the whole Nyquist
'onesided' uses half the Nyquist
mscohere(...) plots the
magnitude squared coherence versus frequency in the current figure
Note If you estimate the magnitude squared coherence with a single window, or section, the value is identically 1 for all frequencies . You must use at least two sections.
Compute and plot the coherence estimate between two colored noise sequences,
y. Reset the random number generator for reproducible results. Use a Hann window to estimate the coherence.
rng default r = randn(16384,1); h1 = ones(1,10)/sqrt(10); x = filter(h1,1,r); h = fir1(30,0.2,rectwin(31)); y = filter(h,1,x); mscohere(x,y,hanning(1024),512,1024)
The magnitude squared coherence estimate is a function of frequency
with values between 0 and 1 that indicates how well
y at each frequency. The magnitude squared coherence
is a function of the power spectral densities, Pxx(f) and Pyy(f),
and the cross power spectral density, Pxy(f),
 Stoica, Petre, and Randolph Moses. Spectral Analysis of Signals. Upper Saddle River, NJ: Prentice Hall, 2005.
 Kay, Steven M. Modern Spectral Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1988.
 Rabiner, Lawrence R., and Bernard Gold. Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
 Welch, Peter D. "The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms." IEEE® Transactions on Audio and Electroacoustics. Vol. AU-15, 1967, pp. 70–73.