Sampling and Reconstruction of Multiband Signals in Multiresolution Subspaces Associated With the Fractional Wavelet Transform

The fractional wavelet transform (FrWT), which generalizes the ordinary wavelet transform, is a very promising tool for signal processing and analysis. A sampling theory for signals in FrWT-based multiresolution subspaces has been proposed recently. However, the signals to be sampled are regarded as lowpass signals indiscriminately. When dealing with bandpass or multiband signals, the sampling rate could be unnecessarily high. This letter investigates the sampling theory of multiband signals in multiresolution subspaces associated with the FrWT. The nonideal sampling and reconstruction scheme we proposed can guarantee lower sampling rate, fewer sampling points but subequal reconstruction performances. Numerical experiments are presented to validate the theoretical derivations.