Abstract: A method and modem receiver for receiving serial data from a transmission link, for recovering data from the received data, and for synchronizing the receiver timing to that of the transmitter are disclosed. A receiver equalizer includes a filter and quantizer in the forward path and a feedback circuit connecting the quantizer output to the filter input. A measuring circuit is used to initialize the feedback circuit. The receiver filter, provided as a QMF wavelet filter bank, is implemented in one embodiment with a form of polyphase filtering followed by four M/2-point FFTs. The quantizer recovers data symbols and provides a quantization error feedback signal. The measuring circuit provides an approximation of phase and amplitude of isolated wavelets.

Abstract: A method for communicating serial input data over a transmission link. Serial input data is partitioned into parallel data elements and is coded prior to rotation by an invertible linear mapping. Resulting frames of parallel sign elements are transmitted over the link. After receipt from the link, the signal is assembled into frames of parallel signal elements which are de-rotated by an inverse linear mapping, then decoded. Thresholding the result of the inverse mapping recovers the parallel data elements, which are then re-assembled into serial output data. The linear mapping employs: 1) commuting rotation matrices for convolutionally rotating data vectors into signal vectors and vice-versa; 2) filter bank polyphase rotation matrices; or 3) computationally efficient multi-rate wavelet filter banks. Coefficients of the rotation matrix of the receiver are adaptively equalized to correct for transmission path distortion.