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# scipy.signal.convolve

`scipy.signal.``convolve`(in1, in2, mode='full', method='auto')

  Convolve two N-dimensional arrays.

  Convolve 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 convolution 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 convolution.

  > `direct`

  >   The convolution is determined directly from sums, the definition of convolution.

  > `fft`

  >   The Fourier Transform is used to perform the convolution by calling `fftconvolve`.

  > `auto`

  >   Automatically chooses direct or Fourier method based on an estimate of which is faster (default). See Notes for more detail.

  >   New in version 0.19.0.

  Returns:

  convolve : array

  > An N-dimensional array containing a subset of the discrete linear convolution of in1 with in2.

  See also

  `numpy.polymul`
    performs polynomial multiplication (same operation, but also accepts poly1d objects)
  `choose_conv_method`
    chooses the fastest appropriate convolution method

  `fftconvolve`

  Notes

  By default, `convolve` and `correlate` use `method='auto'`, which calls `choose_conv_method` to choose the fastest method using pre-computed values (`choose_conv_method` can also measure real-world timing with a keyword argument). Because `fftconvolve` relies on floating point numbers, there are certain constraints that may force method=direct (more detail in `choose_conv_method` docstring).

  Examples

  Smooth a square pulse using a Hann window:

      >>> from scipy import signal
      >>> sig = np.repeat([0., 1., 0.], 100)
      >>> win = signal.hann(50)
      >>> filtered = signal.convolve(sig, win, mode='same') / sum(win)

      >>> import matplotlib.pyplot as plt
      >>> fig, (ax_orig, ax_win, ax_filt) = plt.subplots(3, 1, sharex=True)
      >>> ax_orig.plot(sig)
      >>> ax_orig.set_title('Original pulse')
      >>> ax_orig.margins(0, 0.1)
      >>> ax_win.plot(win)
      >>> ax_win.set_title('Filter impulse response')
      >>> ax_win.margins(0, 0.1)
      >>> ax_filt.plot(filtered)
      >>> ax_filt.set_title('Filtered signal')
      >>> ax_filt.margins(0, 0.1)
      >>> fig.tight_layout()
      >>> fig.show()

  (Source code)