Patent ID: 7558310

Claim:
A method for implementation of multi-resolution complex Wavelet waveforms in the Fourier domain and orthogonal Wavelet division multiple access (OWDMA) filter banks, said method comprising: deriving a single multi-resolution Wavelet implementation using design coordinates in the frequency domain to provide multi-resolution property for Wavelets at multiple scales and translations; changing said Wavelet to a complex Wavelet in the Fourier frequency domain by incorporating a frequency translation as a Wavelet parameter in addition to existing scale (dilation) and translation (shift) parameters; deriving said complex Wavelet with flexibility to meet filter design requirements; constructing OWDMA filters and filter banks implemented with said complex Wavelet waveforms over frequency bands for simultaneous implementation of multi-resolution OWDMA filters at different scales and different frequencies and different symbol rates; using said complex Wavelet to generate a multi-resolution mother Wavelet at dc using design coordinates in the frequency domain which enable the generation of a desired multi-resolution complex Wavelet using appropriate scale, frequency, and translation changes to the mother Wavelet; and implementing said OWDMA filters in a communications transmitter and in a communications receiver for a communications link.