# Adaptive knot selection for B-spline fitting

When fitting a B-spline for regression purposes I've seen a lot of cases where knots are fixed uniformly ,but in some situations this could lead to poor estimations because the behaviour of the curve is not uniform. Knots should be denser when function changes rapidly to capture those "high frequency" moves. I've read some papers that propose different methods to fit adaptive knots, by pruning knots , by fitting multi-resolution basis, etc. My idea (it's just that, an idea) is to use the short time Fourier transform to determine the intervals where higher frequencies are present, and hence to fix denser knots in these, and on the other hand to figure out where the low frequencies are more important and hence to fix more sparse knots. Is this theoretically correct? Maybe it's already been done , but honestly I didn't find anything online. Any hint or suggestions will be greatly appreciated.

• One fly in the ointment would be to distinguish between noise and signal such that having a noise model would be contributory toward a proper solution. – Carl Dec 5 '18 at 6:14