Multi-channel wavelet codec
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.
1. A method for encoding, pulse shaping, modulating, and transmitting a signal in a communication system, the method comprising:
selecting, by a transmitter control system, an analysis wavelet filter bank that is adaptive and capable of encoding, pulse shaping, and modulating the signal;
recursively generating, by the transmitter control system, low-pass and high-pass filters according to the analysis wavelet filter bank;
re-ordering the low-pass and high-pass filters according to frequency by the analysis wavelet filter bank, wherein re-ordering the low-pass and high-pass filters includes:
pairing a plurality of high-pass filters and a plurality of low-pass filters to form a plurality of filter bank pairs, wherein the analysis wavelet filter bank is in a stage of recursion;
numbering said plurality of filter bank pairs;
ordering even numbered filter bank pairs such that an even numbered input to each of the even numbered filter bank pairs are filtered with a low-pass filter, and an odd numbered input to each of the even numbered filter bank pairs are filtered with a high-pass filter; and
reordering odd numbered filter bank pairs such that an odd numbered input to each of the odd numbered filter bank pairs are filtered with a low-pass filter, and an even numbered input to each of the odd numbered filter bank pairs are filtered with a high-pass filter;
selecting values from the signal with the analysis wavelet filter bank;
using the selected values for modulating the low-pass and high-pass filters; and
combining the modulated low-pass and high-pass filters to output an encoded signal.
2. The method of claim 1 further comprising the step of:
transmitting from a transmitter the encoded signal from the combined modulated low-pass and high-pass filters in base-band.
3. The method of claim 1 further comprising the step of:
using the encoded signal from the low-pass and high-pass filters to modulate a carrier for transmitting the encoded signal.
4. The method of claim 1 further comprising the steps of:
aggregating an encoded binary data stream into a plurality of symbols having an unequal number of bits per symbol depending upon a channel quality; and
creating the encoded signal from the plurality of symbols.
5. A method for demodulating, pulse shaping, and decoding a transmitted signal in a communication system, the method comprising:
selecting, by a receiver control system, a synthesis wavelet filter bank that is adaptive and capable of demodulating, pulse shaping, and decoding a transmitted signal;
receiving the transmitted signal to produce a received signal;
recursively generating, by the receiver control system, low-pass and high-pass filters according to the synthesis wavelet filter bank;
re-ordering the low-pass and high-pass filters according to frequency by the synthesis wavelet filter bank, wherein re-ordering the low-pass and high-pass filters includes:
pairing a plurality of high-pass filters and a plurality of low-pass filters to form a plurality of filter bank pairs, wherein the synthesis wavelet filter bank is in a stage of recursion;
numbering said plurality of filter bank pairs;
ordering even numbered filter bank pairs such that an even numbered input to each of the even numbered filter bank pairs are filtered with a low-pass filter, and an odd numbered input to each of the even numbered filter bank pairs are filtered with a high-pass filter; and
reordering odd numbered filter bank pairs such that an odd numbered input to each of the odd numbered filter bank pairs are filtered with a low-pass filter, and an even numbered input to each of the odd numbered filter bank pairs are filtered with a high-pass filter;
recursively filtering the received signal with the reordered low-pass and high-pass filters by the synthesis wavelet filter bank; and
decoding symbols from the recursively filtered signal by the synthesis wavelet filter bank.
6. The method of claim 5 , wherein receiving the transmitted signal further comprises demodulating a carrier by the synthesis wavelet filter bank.
7. The method of claim 5 further comprising the steps of:
disaggregating the symbols to produce a decoded binary data stream.
8. The method of claim 5 , wherein the recursively filtering step further comprises:
filtering the received signal with the low-pass and high-pass filters in a first stage of recursion to produce recursively filtered signals comprising a low-pass and a high-pass filtered signals; and
filtering in a second stage the low-pass and high-pass filtered signals with the low-pass and high-pass filters;
filtering in a third stage the low-pass and high-pass filtered signals with the low-pass and high-pass filters; and
filtering in a fourth stage the low-pass and high-pass filtered signals with the low-pass and high-pass filters.
9. The method of claim 5 , wherein numbering said plurality of filter bank pairs includes numbering inputs to each of the plurality of filter bank pairs.
10. The method of claim 5 , further comprising adding delay to inputs to each of the plurality of filter bank pairs wherein the synthesis wavelet filter bank is in a stage of recursion.
11. A method for encoding, pulse-shaping, and modulating transmitted signal values in a communication system, the method comprising:
selecting, by a transmitter control system, an analysis wavelet filter bank that is adaptive and capable of encoding, pulse shaping, and modulating a signal on the transmitter side;
recursively generating, by the transmitter control system, low-pass and high-pass filters in a plurality of stages according to the analysis wavelet filter bank;
re-ordering the low-pass and high-pass filters within at least two of the plurality of stages according to frequency, wherein re-ordering the low-pass and high-pass filters includes:
pairing a plurality of high-pass filters and a plurality of low-pass filters to form a plurality of filter bank pairs, wherein the analysis wavelet filter bank is in a stage of recursion;
numbering said plurality of filter bank pairs;
ordering even numbered filter bank pairs such that an even numbered input to each of the even numbered filter bank pairs are filtered with a low-pass filter, and an odd numbered input to each of the even numbered filter bank pairs are filtered with a high-pass filter; and
reordering odd numbered filter bank pairs such that an odd numbered input to each of the odd numbered filter bank pairs are filtered with a low-pass filter, and an even numbered input to each of the odd numbered filter bank pairs are filtered with a high-pass filter;
selecting values from the signal by the analysis wavelet filter bank;
using the selected values for modulating low-pass and high-pass filters; and
combining the modulated low-pass and high-pass filters to output an encoded signal.
12. The method of claim 11 further comprising the steps of:
aggregating an encoded binary data stream into a plurality of symbols having an unequal number of bits per symbol depending upon a channel quality; and
creating the encoded signal from the plurality of symbols.
13. The method of claim 11 further comprising the step of:
transmitting the encoded signal from the combined low-pass and high-pass filters in base band.