Convolution is often used for smoothing noisy data; a typical use will keep the 'same' length of data and may look like this:
> convol = 2**-np.linspace(-2,2,100)**2; > y2 = np.convolve(y,convol/np.sum(convol), mode='same') ## simple smoothing > ax.plot(x, y2, label="simple smoothing", color='g') However, when the smoothed curve has some nonzero background value at its edges, this convolution mode internally pads it with zeros, resulting in the curve looking like moustache of Frank Zappa. I made an example plot illustrating this here: https://www.fzu.cz/~dominecf/misc/numpy_smoothing_example.png. Such a result, i.e. the green curve, is not publication ready! 1) One way around is to np.pad(..., mode='edge'), then convolve & properly truncate the curve back to its original length. This is not a correct approach, however, as it makes the curve edges smooth, but their actual shape becomes very sensitive to the pointwise noise. Moreover, it artificially removes the curve's slope at its edges. 2) Another way around is to generate an auxiliary "Zappa's moustache" by applying the same convolution to a fresh array of np.ones_like(y). Then one can normalize the convolved curve by this auxiliary function. This has only one downside of keeping the curve more noisy at its edges, which however appears more scientifically honest to me - at the dataset edges one simply has less means to filter out noise. > convol = 2**-np.linspace(-2,2,100)**2; > norm = np.convolve(np.ones_like(y),convol/np.sum(convol), mode='same') > y2 = np.convolve(y,convol/np.sum(convol), mode='same')/norm ## simple > smoothing > ax.plot(x, y2, label="approach 2", color='k') In my experimental work, I am missing this behaviour of np.convolve in a single function. I suggest this option should be accessible numpy under the mode="normalized" option. (Actually I believe this could have been set as default, but this would break compatibility.) Thanks for consideration, Filip _______________________________________________ NumPy-Discussion mailing list -- numpy-discussion@python.org To unsubscribe send an email to numpy-discussion-le...@python.org https://mail.python.org/mailman3/lists/numpy-discussion.python.org/ Member address: arch...@mail-archive.com
