Periodic multiresolution analysis using quasi-orthogonals splines

We present a periodic spline quasi-wavelet generated from a quasi-orthogonal spline basis. By construction the quasi-wavelet and related multiresolution spaces are approximately orthogonal. The quasi-wavelet allows for multiresolution decomposition using a single scaling function. This is in contrast with classic periodic wavelets which require a different scaling function between each resolution. This results in a fast algorithm to create the periodic multiresolution pyramid of least squares fits to periodic data.