Systems, methods, and apparatus for denoising signals

1 . An apparatus comprising:

a first denoiser configured to receive an input signal and to generate a denoised signal, wherein the denoised signal includes near-zero phase error and near-zero phase delay;

a signal reverser configured to receive the input signal and to generate a time reversed signal;

a second denoiser configured to receive the time reversed signal and to generate a denoised time reversed signal, wherein the denoised time reversed signal includes near-zero phase error and near-zero phase delay; and

a signal combiner configured to add the denoised signal and the denoised time reversed signal to generate an output signal.

2 . The apparatus according to claim 1 , further comprising a receiver configured to receive a mixture of signals, wherein the receiver is configured to digitize the mixture of signals to generate the input signal, and wherein the mixture of signals comprises a noise signal and one or more waveform signals from one or more sources.

3 . The apparatus according to claim 2 , further comprising an antenna configured to receive radio frequency (RF) signals or radar signals and to generate the mixture of signals.

4 . The apparatus according to claim 2 , wherein the receiver includes an analog-to-digital converter (ADC), and wherein the ADC is configured to digitize the mixture of signals to generate the input signal.

5 . The apparatus according to claim 4 , wherein the receiver further comprises an amplifier that amplifies the mixture of signals before the mixture of signals is received by the ADC, and wherein the amplifier amplifies the mixture of signals to a predetermined amplitude for sampling by the ADC.

6 . The apparatus according to claim 1 , wherein the input signal is a time-series of data points of a mixture of signals, wherein the denoised signal is an estimate of a signal of interest, and wherein the denoised time reversed signal is an estimate of a time reversal of the signal of interest.

7 . The apparatus according to claim 1 , wherein the first denoiser includes a first multi-pole filter, wherein the first multi-pole filter is configured to filter and/or shape the input signal, and wherein the second denoiser includes a second multi-pole filter, wherein the second multi-pole filter is configured to filter and/or shape the denoised reversed time signal.

8 . The apparatus according to claim 1 , wherein the first denoiser is configured to process the input signal using a first neural network to generate the denoised signal, and wherein the second denoiser is configured to process the time reversed signal using a second neural network to generate the denoised time reversed signal.

9 . The apparatus according to claim 1 , wherein the first denoiser comprises a plurality of neural network reservoirs that interact with each other to enhance detection of the input signal, and wherein the second denoiser comprises a plurality of neural network reservoirs that interact with each other to enhance detection of the input signal.

10 . The apparatus according to claim 1 , wherein the first denoiser is configured to:

linearly map the input signal to reservoir states of a dynamical reservoir;

generate a high-dimensional state-space representation of the input signal by combining the input signal with the reservoir states;

denoise the reservoir states by removing noise from each reservoir state signal; and

generate the denoised signal by combining the denoised reservoir states.

11 . The apparatus according to claim 10 , wherein the second denoiser is configured to:

linearly map the time reversed signal to reservoir states of a dynamical reservoir;

generate a high-dimensional state-space representation of the time reversed signal by combining the time reversed signal with the reservoir states;

denoise the reservoir states by removing noise from each reservoir state signal; and

generate the denoised time reversed signal by combining the denoised reservoir states.

12 . The apparatus according to claim 1 , further comprising a transmitter for transmitting a radio frequency (RF) signal or a radar signal.

13 . A method comprising:

denoising, at one or more denoisers, an input signal to generate a denoised signal, wherein the denoised signal includes near-zero phase error and near-zero phase delay;

performing a time-reversal operation on the input signal to generate a time reversed signal of the input signal;

denoising, at the one or more denoisers, the time reversed signal to generate a denoised time reversed signal, wherein the denoised time reversed signal includes near-zero phase error and near-zero phase delay; and

generating an output signal based on adding the denoised signal and the denoised time revered signal.

14 . The method according to claim 13 , wherein the input signal is a time-series of data points of a mixture of signals, wherein the denoised signal is an estimate of a signal of interest, and wherein the denoised time reversed signal is an estimate of a time reversal of the signal of interest.

15 . The method according to claim 13 , further comprising generating the input signal based on a mixture of signals, and wherein the mixture of signals comprises a noise signal and one or more waveform signals from one or more sources.

16 . The method according to claim 13 , wherein the one or more denoisers includes a first denoiser and a second denoiser, wherein the first denoiser includes a first multi-pole filter, wherein the first multi-pole filter is configured to filter and/or shape the input signal, and wherein the second denoiser includes a second multi-pole filter, wherein the second multi-pole filter is configured to filter and/or shape the denoised reversed time signal.

17 . The method according to claim 13 , wherein denoising the input signal further comprises processing the input signal using a first neural network, and wherein denoising the time reversed signal further includes processing the time reversed signal using a second neural network.

18 . The method according to claim 13 , wherein the one or more denoisers comprise a plurality of neural network reservoirs that interact with each other to enhance detection of the input signal.

19 . The method according to claim 13 , wherein denoising the input signal comprises:

linearly mapping the input signal to reservoir states of a dynamical reservoir;

generating a high-dimensional state-space representation of the input signal by combining the input signal with the reservoir states;

denoising the reservoir states by removing noise from each reservoir state signal; and

generating the denoised signal by combining the denoised reservoir states.

20 . A non-transitory computer-readable medium having stored thereon instruction code, wherein the instruction code is executable by one or more processors to perform operations comprising:

denoising an input signal to generate a denoised signal, wherein the denoised signal includes near-zero phase error and near-zero phase delay;

generating a time reversed signal of the input signal;

denoising the time reversed signal to generate a denoised time reversed signal, wherein the denoised time reversed signal includes near-zero phase error and near-zero phase delay; and

generating an output signal by adding the denoised signal and the denoised time revered signal.