Inversion of channel distortion by adaptive wavelet lifting
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.
1. A method for correcting a channel distortion of a known signal sent by a transmitter and received by a receiver, the method comprising the steps of:
(a) decomposing a message sent by the transmitter with a transmitter filter bank, the decomposition comprising transmitter filter coefficients;
(b) computing a novelty signal from a difference between a transmitted signal and a received signal;
(c) decomposing the novelty signal by the receiver with a receiver filter bank, the decomposition comprising receiver filter coefficients; and
(d) computing an inverse receiver filter coefficients that represent the novelty signal;
wherein the channel distortion is corrected by the inverse receiver filter coefficients.
2. The method according to claim 1 wherein the transmitter filter bank utilizes wavelet lifting.
3. The method according to claim 1 wherein the receiver filter bank utilizes wavelet lifting.
4. The method according to claim 1 wherein the transmitter filter bank and the receiver filter bank are identical.
5. A method for inverting distortion processes in a telecommunication channel, the method comprising the steps of:
(a) constructing a signal from a message in a transmitter using a first wavelet filter bank;
(b) sending the signal to a receiver, wherein the signal is known to the receiver;
(c) comparing in the receiver the signal with an expected signal to form a novelty signal;
(d) if the novelty signal is greater than a predetermined signal level, using by the receiver a second wavelet filter bank that is known to the transmitter to compute coefficients that are required to represent the novelty signal in terms of the second wavelet filter bank;
(e) computing coefficients of an inverse wavelet filter bank to the second wavelet filter bank;
(f) updating by the transmitter the first wavelet filter bank using the coefficients of the inverse wavelet filter bank;
(g) constructing by the transmitter an updated signal using the updated first wavelet filter bank; and
(h) sending the updated signal to the receiver.
6. The method according to claim 5 further comprising the step of: processing the updated signal by repeating steps (c) through (h).
7. The method according to claim 5 wherein the first wavelet filter bank utilizes wavelet lifting.
8. The method according to claim 5 wherein the second wavelet filter bank utilizes wavelet lifting.
9. The method according to claim 5 wherein the expected signal is known to the receiver and has been distorted by the telecommunication channel in a manner expected by the receiver.
10. The method according to claim 5 wherein step (e) further comprises the step of:
computing coefficients of a synthesis wavelet filter bank that is related to the second wavelet filter bank, wherein the synthesis wavelet filter bank is the inverse wavelet filter bank to the second wavelet filter bank.
11. The method according to claim 5 further comprising the step of: selecting by the receiver an analysis wavelet filter bank that is amenable to analyzing the novelty signal.
12. The method according to claim 5 wherein the first wavelet filter bank and the second wavelet filter bank are identical.
13. The method according to claim 5 wherein said step (a) further comprises the step of:
constructing the signal as a base-band signal that is sent directly over the telecommunication channel.
14. The method according to claim 5 wherein said step (a) further comprises the step of:
constructing the signal as a base-band signal that is used to modulate a carrier associated with the telecommunication channel.
15. The method according to claim 5 wherein said comparing step (c) further comprises the steps of:
de-noising the signal received in the receiver using soft thresholding to yield a second signal; and
computing the novelty signal by subtracting the second signal from the expected signal.
16. A method for inverting distortion processes in a telecommunication channel, the method comprising the steps of:
(a) constructing a signal from a message in a transmitter using a first wavelet filter bank;
(b) sending the signal to a receiver, wherein the signal is known to the receiver;
(c) comparing in the receiver the signal with an expected signal to form a novelty signal;
(d) if the novelty signal is greater than a predetermined signal level, using by the receiver a second wavelet filter bank that is known to the transmitter to compute coefficients that are required to represent the novelty signal in terms of the second wavelet filter bank;
(e) computing coefficients of an inverse wavelet filter bank to the second wavelet filter bank;
(f) computing by the transmitter an updated message utilizing the first wavelet filter bank and the coefficients of the inverse wavelet filter bank;
(g) constructing by the transmitter an updated signal using the updated message and the first wavelet filter bank; and
(h) sending the updated signal to the receiver.
17. The method according to claim 16 further comprising the step of:
processing the updated signal by repeating steps (c) through (h).
18. The method according to claim 16 wherein the first wavelet filter bank utilizes wavelet lifting.
19. The method according to claim 16 wherein the second wavelet filter bank utilizes wavelet lifting.
20. The method according to claim 16 wherein the expected signal is known to the receiver and has been distorted by the telecommunication channel in a manner expected by the receiver.
21. The method according to claim 16 wherein step (f) further comprises the step of:
computing coefficients of a synthesis wavelet filter bank that is related to the second wavelet filter bank, wherein the synthesis wavelet filter bank is the inverse wavelet filter bank to the second wavelet filter bank.
22. The method according to claim 16 further comprising the step of: selecting by the receiver an analysis wavelet filter bank that is amenable to analyzing the novelty signal.
23. The method according to claim 16 wherein the first wavelet filter bank and the second wavelet filter bank are identical.
24. The method according to claim 16 wherein said step (a) further comprises the step of:
constructing the signal as a base-band signal that is sent directly over the telecommunication channel.
25. The method according to claim 16 wherein said step (a) further comprises the step of:
constructing the signal as a base-band signal that is used to modulate a carrier associated with the telecommunication channel.
26. The method according to claim 16 wherein said comparing step (c) further comprises the steps of:
de-noising the signal received in the receiver using soft thresholding to yield a second signal; and
computing the novelty signal by subtracting the second signal from the expected signal.