correlate(a, v, mode='valid')
This function computes the correlation as generally defined in signal processing texts:
c_{av}[k] = sum_n a[n+k] * conj(v[n])
with a and v sequences being zero-padded where necessary and conj being the conjugate.
The definition of correlation above is not unique and sometimes correlation may be defined differently. Another common definition is:
c'_{av}[k] = sum_n a[n] conj(v[n+k])
which is related to c_{av}[k]
by c'_{av}[k] = c_{av}[-k]
.
numpy.correlate
may perform slowly in large arrays (i.e. n = 1e5) because it does not use the FFT to compute the convolution; in that case, scipy.signal.correlate
might be preferable.
Input sequences.
Refer to the convolve
docstring. Note that the default is 'valid', unlike convolve
, which uses 'full'.
:None:None:`old_behavior`
was removed in NumPy 1.10. If you need the old behavior, use :None:None:`multiarray.correlate`
.
Cross-correlation of two 1-dimensional sequences.
convolve
Discrete, linear convolution of two one-dimensional sequences.
multiarray.correlate
Old, no conjugate, version of correlate.
scipy.signal.correlate
uses FFT which has superior performance on large arrays.
>>> np.correlate([1, 2, 3], [0, 1, 0.5]) array([3.5])
>>> np.correlate([1, 2, 3], [0, 1, 0.5], "same") array([2. , 3.5, 3. ])
>>> np.correlate([1, 2, 3], [0, 1, 0.5], "full") array([0.5, 2. , 3.5, 3. , 0. ])
Using complex sequences:
>>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full') array([ 0.5-0.5j, 1.0+0.j , 1.5-1.5j, 3.0-1.j , 0.0+0.j ])
Note that you get the time reversed, complex conjugated result when the two input sequences change places, i.e., c_{va}[k] = c^{*}_{av}[-k]
:
>>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full') array([ 0.0+0.j , 3.0+1.j , 1.5+1.5j, 1.0+0.j , 0.5+0.5j])See :
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.ma.core.correlate
numpy.correlate
matplotlib.pyplot.acorr
matplotlib.axes._axes.Axes.xcorr
matplotlib.pyplot.xcorr
scipy.signal._max_len_seq.max_len_seq
matplotlib.axes._axes.Axes.acorr
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