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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def fftconvolve(in1, in2, mode="full", axis=None):
 """ Convolve two N-dimensional arrays using FFT. See convolve. This is a fix of scipy.signal.fftconvolve, adding an axis argument and importing locally the stuff only needed for this function """

    s1 = np.array(in1.shape)
    s2 = np.array(in2.shape)
    complex_result = (np.issubdtype(in1.dtype, np.complexfloating) or
                      np.issubdtype(in2.dtype, np.complexfloating))

    if axis is None:
        size = s1 + s2 - 1
        fslice = tuple([slice(0, int(sz)) for sz in size])
    else:
        equal_shapes = s1 == s2
        # allow equal_shapes[axis] to be False
        equal_shapes[axis] = True
        assert equal_shapes.all(), 'Shape mismatch on non-convolving axes'
        size = s1[axis] + s2[axis] - 1
        fslice = [slice(l) for l in s1]
        fslice[axis] = slice(0, int(size))
        fslice = tuple(fslice)

    # Always use 2**n-sized FFT
    fsize = 2 ** int(np.ceil(np.log2(size)))
    if axis is None:
        IN1 = fftpack.fftn(in1, fsize)
        IN1 *= fftpack.fftn(in2, fsize)
        ret = fftpack.ifftn(IN1)[fslice].copy()
    else:
        IN1 = fftpack.fft(in1, fsize, axis=axis)
        IN1 *= fftpack.fft(in2, fsize, axis=axis)
        ret = fftpack.ifft(IN1, axis=axis)[fslice].copy()
    del IN1
    if not complex_result:
        ret = ret.real
    if mode == "full":
        return ret
    elif mode == "same":
        if np.product(s1, axis=0) > np.product(s2, axis=0):
            osize = s1
        else:
            osize = s2
        return signaltools._centered(ret, osize)
    elif mode == "valid":
        return signaltools._centered(ret, abs(s2 - s1) + 1)