# scipy.signal.correlate¶

scipy.signal.correlate(in1, in2, mode='full', method='auto')[source]

Cross-correlate two N-dimensional arrays.

Cross-correlate in1 and in2, with the output size determined by the mode argument.

Parameters: in1 : array_like First input. in2 : array_like Second input. Should have the same number of dimensions as in1. mode : str {‘full’, ‘valid’, ‘same’}, optional A string indicating the size of the output: full The output is the full discrete linear cross-correlation of the inputs. (Default) valid The output consists only of those elements that do not rely on the zero-padding. In ‘valid’ mode, either in1 or in2 must be at least as large as the other in every dimension. same The output is the same size as in1, centered with respect to the ‘full’ output. method : str {‘auto’, ‘direct’, ‘fft’}, optional A string indicating which method to use to calculate the correlation. direct The correlation is determined directly from sums, the definition of correlation. fft The Fast Fourier Transform is used to perform the correlation more quickly (only available for numerical arrays.) auto Automatically chooses direct or Fourier method based on an estimate of which is faster (default). See convolve Notes for more detail. New in version 0.19.0. correlate : array An N-dimensional array containing a subset of the discrete linear cross-correlation of in1 with in2.

choose_conv_method
contains more documentation on method.

Notes

The correlation z of two d-dimensional arrays x and y is defined as:

z[...,k,...] = sum[..., i_l, ...] x[..., i_l,...] * conj(y[..., i_l - k,...])


This way, if x and y are 1-D arrays and z = correlate(x, y, 'full') then

$z[k] = (x * y)(k - N + 1) = \sum_{l=0}^{||x||-1}x_l y_{l-k+N-1}^{*}$

for $$k = 0, 1, ..., ||x|| + ||y|| - 2$$

where $$||x||$$ is the length of x, $$N = \max(||x||,||y||)$$, and $$y_m$$ is 0 when m is outside the range of y.

method='fft' only works for numerical arrays as it relies on fftconvolve. In certain cases (i.e., arrays of objects or when rounding integers can lose precision), method='direct' is always used.

Examples

Implement a matched filter using cross-correlation, to recover a signal that has passed through a noisy channel.

>>> from scipy import signal
>>> sig = np.repeat([0., 1., 1., 0., 1., 0., 0., 1.], 128)
>>> sig_noise = sig + np.random.randn(len(sig))
>>> corr = signal.correlate(sig_noise, np.ones(128), mode='same') / 128

>>> import matplotlib.pyplot as plt
>>> clock = np.arange(64, len(sig), 128)
>>> fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, sharex=True)
>>> ax_orig.plot(sig)
>>> ax_orig.plot(clock, sig[clock], 'ro')
>>> ax_orig.set_title('Original signal')
>>> ax_noise.plot(sig_noise)
>>> ax_noise.set_title('Signal with noise')
>>> ax_corr.plot(corr)
>>> ax_corr.plot(clock, corr[clock], 'ro')
>>> ax_corr.axhline(0.5, ls=':')
>>> ax_corr.set_title('Cross-correlated with rectangular pulse')
>>> ax_orig.margins(0, 0.1)
>>> fig.tight_layout()
>>> fig.show()


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