#### Previous topic

scipy.signal.correlate

#### Next topic

scipy.signal.convolve2d

# scipy.signal.fftconvolve

`scipy.signal.``fftconvolve`(in1, in2, mode='full')

  Convolve two N-dimensional arrays using FFT.

  Convolve in1 and in2 using the fast Fourier transform method, with the output size determined by the mode argument.

  This is generally much faster than `convolve` for large arrays (n > ~500), but can be slower when only a few output values are needed, and can only output float arrays (int or object array inputs will be cast to float).

  Parameters: | in1 : array_like First input. in2 : array_like Second input. Should have the same number of dimensions as in1; if sizes of in1 and in2 are not equal then in1 has to be the larger array. 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. `same` The output is the same size as in1, centered with respect to the ‘full’ output.
  Returns: | out : array An N-dimensional array containing a subset of the discrete linear convolution of in1 with in2.

  Examples

  Autocorrelation of white noise is an impulse. (This is at least 100 times as fast as `convolve`.)

      >>> from scipy import signal
      >>> sig = np.random.randn(1000)
      >>> autocorr = signal.fftconvolve(sig, sig[::-1], mode='full')

      >>> import matplotlib.pyplot as plt
      >>> fig, (ax_orig, ax_mag) = plt.subplots(2, 1)
      >>> ax_orig.plot(sig)
      >>> ax_orig.set_title('White noise')
      >>> ax_mag.plot(np.arange(-len(sig)+1,len(sig)), autocorr)
      >>> ax_mag.set_title('Autocorrelation')
      >>> fig.tight_layout()
      >>> fig.show()

  Gaussian blur implemented using FFT convolution. Notice the dark borders around the image, due to the zero-padding beyond its boundaries. The `convolve2d` function allows for other types of image boundaries, but is far slower.

      >>> from scipy import misc
      >>> lena = misc.lena()
      >>> kernel = np.outer(signal.gaussian(70, 8), signal.gaussian(70, 8))
      >>> blurred = signal.fftconvolve(lena, kernel, mode='same')

      >>> fig, (ax_orig, ax_kernel, ax_blurred) = plt.subplots(1, 3)
      >>> ax_orig.imshow(lena, cmap='gray')
      >>> ax_orig.set_title('Original')
      >>> ax_orig.set_axis_off()
      >>> ax_kernel.imshow(kernel, cmap='gray')
      >>> ax_kernel.set_title('Gaussian kernel')
      >>> ax_kernel.set_axis_off()
      >>> ax_blurred.imshow(blurred, cmap='gray')
      >>> ax_blurred.set_title('Blurred')
      >>> ax_blurred.set_axis_off()
      >>> fig.show()

  (Source code)