I've been working with wavelets for a project (specifically implementing the Fast Wavelet Transform for the family of Biorthogonal B-Spline Wavelets with d = d_ tilde = 2), and I noticed something weird with the filter coefficients.

In the documentation, it specifies that: The primal highpass filter coefficients satisfy b _ n = (-1)^n * (a _ tilde) _ n, where (a _ tilde) _ n are dual lowpass filter coefficients. However, I noticed that the filter coefficients provided don't actually seem to satisfy this condition. For example, if n=0 (corresponding to b0), it is supposed to equal (-1)^0 * (a _ tilde)1-0 = (-1)^0 * (a _ tilde)_1 = 1/4, but it actually equals -1/4. I am wondering if anyone knows why this is the case, and if there's something I'm missing or misinterpreting.

Thank you!