Fractional (α,τ)spline wavelet demo  Screenshot 
This applet demonstrates a new wavelet transform that is based on an extended family of fractional splines. The implementation uses a new FFTbased algorithm that can handle IIR filters efficiently. The applet displays the scaling and wavelet basis functions; they can be modified interactively. The transform can be applied to an image in a separable fashion, and then reverted exactly. The parameters are :


To the best of our knowledge, these are the first examples ever of a wavelet transform with a fractional order of approximation.  
Reference: T. Blu, M. Unser, "A Complete Family of Scaling Functions: The (α, τ)Fractional Splines," Proceedings of the TwentyEighth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'03), Hong Kong SAR, People's Republic of China, April 610, 2003, in press. 

Fractional wavelet demo  Screenshot 
This demo computes a wavelet transform with a continuouslyvarying order parameter α. The underlying scaling functions and wavelets are symmetric. The 2D wavelet transform is separable and implemented by successive filtering and decimation (using Mallat's algorithm) of the rows and columns of the image. Since the filters are not necessarily compactly supported, the decomposition is implemented in the Fourier domain using FFTs. The parameters are :


Reference: T. Blu, M. Unser, "The Fractional Spline Wavelet Transform: Definition and Implementation," Proceedings of the TwentyFifth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), Istanbul, Turkey, June 59, 2000, vol. I, pp. 512515. 