Abstract: Wavelet filters computed from a wavelet transform are used as a means of pulse shaping binary data transmitted and received over multiple parallel channels. At the transmitter the data is parsed from a serial bit stream to several parallel streams. Within each of the parallel bit streams symbols are formed. Signals are created from each symbol by up-sampling by inserting zeros between successive symbols. These signals are passed through a bank of low-pass and high-pass filters derived from a wavelet packet transform. The filters are paired: one high-pass with a low-pass. The ordering is alternated to preserve “natural” frequency ordering. These steps are repeated for this set of signals until only one signal remains. The remaining signal is transmitted in the base band of the transmission system or they are transmitted by modulating the carrier of the transmission system. At the receiver the steps are reversed to recover symbols.

Abstract: A method for inverting telecommunication channel distortion by adaptive wavelet lifting. The distortion signal is analyzed using wavelet lifting and the inverse filter is computed. Coefficients of the inverse filter are used to either compute a transmission pre-filter or to update the transmitted message.

Abstract: Wavelet filters computed from a wavelet transform are used for encoding, transmitting, receiving, and decoding spread spectrum signals on multiple parallel frequency channels. The transmitter encodes the data stream via a mapping to a basis set of wavelets which are orthogonal across the time domain. The spread spectrum data is parsed from a serial bit stream to several parallel streams. The number of bits per symbol need not remain constant. Signals are created from each symbol by first up sampling by inserting zeros between successive symbols. These signals are passed through a bank of low-pass and high-pass filters derived from a wavelet packet transform. The resulting signal is transmitted in the base band of the transmission system, or transmitted by modulating the carrier of the transmission system. At the receiver, the steps are reversed to recover the symbols. Symbol decisions are made through any one of a number of methods.

Abstract: A method for inverting telecommunication channel distortion by adaptive wavelet lifting. The distortion signal is analyzed using wavelet lifting and the inverse filter is computed. Coefficients of the inverse filter are used to either compute a transmission pre-filter or to update the transmitted message.

Abstract: A method for encoding, transmitting, and receiving signals utilizes adaptive wavelet packet trees. A transmitter accepts a binary data stream assumed to be random. At the transmitter the data is parsed from a serial bit stream into several parallel streams. Within each of the parallel bit streams symbols are formed from the bits. Signals are created from each symbol by up-sampling. These signals modulate low-pass and high-pass filters that are derived from a wavelet packet transform (the wavelet and scaling functions, or, equivalently the low-pass and high-pass analysis filters). The filters are paired—one high-pass with one low-pass. The steps recited above are recursively repeated log2 N times for a signal of length N. The resulting signal is transmitted to the receiver. At the receiver, the steps recited above are reversed at the receiver to recover symbols, with the up-sampled signal down-sampled to remove inserted zeroes.

Abstract: An apparatus and method is disclosed for establishing a one-time cryptographic pad between a communicating pair, a communicating pair comprising a pair of transmitter-receivers, each of the pair having a plurality of cryptographic devices in common. The communicating pair also store previously exchanged messages and transmissions, a transmission comprising secure data exchanged by the pair that is independent of message content. The first transmitter-receiver randomly selects a cryptographic device and a previous transmission or message that has been sent to the second transmitter-receiver. The first transmitter-receiver also randomly selects a reference to a message or transmission previously sent by the second transmitter-receiver. The first transmitter-receiver encrypts the previously sent transmission or message and the reference to the message or transmission previously sent by the second transmitter-receiver and sends to the second transmitter-receiver.