[Repost Q] Fast python convolution along one axis only

Not OP. This question is being reposted to preserve technical content removed from elsewhere. Feel free to add your own answers/discussion.

I have two 2-D arrays with the same first axis dimensions. In python, I would like to convolve the two matrices along the second axis only. I would like to get C below without computing the convolution along the first axis as well.

import numpy as np
import scipy.signal as sg

M, N, P = 4, 10, 20
A = np.random.randn(M, N)
B = np.random.randn(M, P)

C = sg.convolve(A, B, 'full')[(2*M-1)/2]

Is there a fast way?