scipy.signal.correlate¶

scipy.signal.
correlate
(in1, in2, mode='full', method='auto')[source]¶ Crosscorrelate two Ndimensional arrays.
Crosscorrelate 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 crosscorrelation of the inputs. (Default)
valid
The output consists only of those elements that do not rely on the zeropadding. 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.
Returns:  correlate : array
An Ndimensional array containing a subset of the discrete linear crosscorrelation of in1 with in2.
See also
choose_conv_method
 contains more documentation on method.
Notes
The correlation z of two ddimensional 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 1D arrays and
z = correlate(x, y, 'full')
then\[z[k] = (x * y)(k  N + 1) = \sum_{l=0}^{x1}x_l y_{lk+N1}^{*}\]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 onfftconvolve
. 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 crosscorrelation, 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('Crosscorrelated with rectangular pulse') >>> ax_orig.margins(0, 0.1) >>> fig.tight_layout() >>> fig.show()