Fast classical and quantum fractional Haar wavelet transforms

The fractional Fourier transform (FRFT) is one-parametric generalization of the classical Fourier transform. FRFT was introduced in the 1980s and found a lot of applications in signal processing. The time and spectral domains are both the special cases of the functional Fourier domain. They correspond to the 0th and 1st fractional Fourier domains, respectively. We introduce the classical and quantum fractional Haar-wavelet transforms and develop corresponding fast algorithms.