Optimal filter-bank wavelet modulation
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 log 2 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.
1. A method for transmitting binary data, the method comprising:
(a) receiving the binary data as a source coded input stream in a first wavelet generator;
(b) pre-selecting by said wavelet generator a wavelet basis from a library of wavelets;
(c) generating a first wavelet packet tree comprising a plurality of pairs of low-pass filters and high-pass filters;
(d) mapping said binary data into a plurality of symbol cells according to said first wavelet packet tree;
(e) modulating at least one pair of low-pass filters and high-pass filters according to the binary data;
(f) alternating the ordering of said at least one pair of low-pass filters and high-pass filters to preserve a natural frequency ordering; and
(g) transmitting from the low-pass and high-pass filters a signal on a communications channel.
2. The method of claim 1 , wherein transmitting comprises modulating a carrier associated with the communications channel.
3. The method of claim 1 , wherein the at least one pair of modulated low-pass and high-pass filters are selected according to a frequency response of the communications channel.
4. The method of claim 1 , wherein the at least one pair of low-pass and high-pass filters are modulated according to a frequency response of the communications channel.
5. The method of claim 1 , wherein said pre-selecting step (b) further comprises pre-selecting a Coiflet wavelet.
6. The method of claim 1 , wherein said pre-selecting step (b) further comprises pre-selecting a Discrete Meyer wavelet.
7. The method of claim 1 , wherein said pre-selecting step (b) further comprises computing said wavelet basis according to an assessment of the communications channel.
8. The method of claim 1 , wherein said transmitting step (g) further comprises transmitting said signal in base-band.
9. The method of claim 1 further comprising the steps of:
receiving said signal in a receiver;
demodulating said signal;
inputting said demodulated signal into an equalizer;
inputting an equalized signal from said equalizer into a second wavelet generator;
generating a second wavelet packet tree that is dual to said first wavelet packet tree to extract said plurality of symbol cells from said equalized signal;
inputting said plurality of symbol cells into a classifier; and
recovering from said classifier said source coded input stream.
10. A system for transmitting binary data, the system comprising:
a transmitter having a first wavelet generator for receiving binary data as a source coded input stream;
a library of wavelets, wherein a wavelet basis is pre-selected by said first wavelet generator from said library of wavelets;
a first wavelet packet tree generated by said first wavelet generator, said first wavelet packet tree having a plurality of pairs of low-pass filters and high-pass filters for mapping said binary data into a plurality of symbol cells according to said first wavelet packet tree, wherein at least one pair of low-pass filters and high-pass filters are modulated according to the binary data and said at least one pair of low-pass filters and high-pass filters are alternated to preserve a natural frequency ordering; and
a communications channel associated with said transmitter for transmitting a signal output from said plurality of pairs of low-pass filters and high-pass filters.
11. A system according to claim 10 wherein the at least one pair of modulated low-pass and high-pass filters are selected according to a frequency response of the communications channel.
12. A system according to claim 10 wherein the at least one pair of low-pass and high-pass filters are modulated according to a frequency response of the communications channel.
13. A system according to claim 10 wherein said pre-selected wavelet basis is a Coiflet wavelet.
14. A system according to claim 10 wherein said pre-selected wavelet basis is a Discrete Meyer wavelet.
15. A system according to claim 10 wherein said wavelet basis is computed according to an assessment of the communications channel.
16. A system according to claim 10 wherein said signal is transmitted in base-band.
17. A system according to claim 10 further comprising:
a receiver for receiving said signal;
a demodulator in said receiver for demodulating said signal;
an equalizer in said receiver for equalizing said demodulated signal;
a second wavelet generator in said receiver having a second wavelet packet tree that is dual to said first wavelet packet tree for receiving said equalized signal and extracting said plurality of symbol cells from said equalized signal;
a classifier in said receiver for recovering said source coded input stream.