Non-linear deterministic stochastic filtering method and system

A system for filtering a whitened noisy input signal (y.sub.k) comprised of an information signal and whitened noise, comprising:

• aposteriori filter means, responsive to the whitened noisy input signal (y.sub.k) comprised of:
• (a) a time delay subsystem for storing the whitened noisy input signal (y.sub.k) over the fixed time delay (T);
• (b) a first non-linear function generator for providing a first non-linear function output ($.sub.k), responsive to raising the whitened noisy input (y.sub.k) by a power of m;
• (c) an FFT subsystem for deriving the FFT of the first nonlinear function output ($.sub.k), for providing both amplitude and phase spectrum outputs;
• (d) a multiplier subsystem for providing a power spectrum output responsive to the amplitude output;
• (e) a zero-mean subsystem responsive to the power spectrum output for providing a zero mean power spectrum output;
• (f) a square rooting subsystem for providing a square rooted zero mean power spectrum output responsive to taking the square root of the zero mean power spectrum output;
• (g) an inverse FFT subsystem responsive to the square rooted zero mean power spectrum output and the FFT phase spectrum output for performing an inverse FFT and providing a new time domain signal output ($.sub.k *) wherein a white noise residual of the whitened noisy input (y.sub.k) is substantially reduced;
• and
• (h) a second non-linear function generator for providing a second non-linear function output (s.sub.k *), responsive to raising a new time domain output ($.sub.k *) by a power of 1/m.

A method for filtering a noisy input comprised of an information-bearing signal and noise where no prior time domain value information or frequency domain parameter value information on the information bearing signal or noise is available and where no separate access to the information bearing signal or to the noise exists, the method comprising:

• (a) passing the noisy input through a whitening filter to render the noise part of the noisy input to become substantially white noise of a flat spectrum over the spectral range of interest and to provide a time domain output;
• (b) applying a non-linear function to the time domain output to provide a non-linear function output;
• (c) Fourier transforming the time domain output over successive finite frames of time to provide a first transformed output;
• (d) Fourier transforming the first transformed output to provide a second transformed output;
• (e) liftering the second transformed output by blocking near zero quefrencies to provide a liftered output;
• (f) inverse Fourier transforming the liftered output to provide an inverse transformed output;
• (g) inverse Fourier transforming the inverse transformed output to provide a new time domain output;
• (h) applying an inverse of the non-linear function to the new time domain output to provide a resultant output;
• (i) passing the resultant output through an inverse whitening filter, to provide a substantially noise-free final output wherein the spectrum of the information bearing signal is unchanged and wherein the noise has been first whitened and then removed.

A system for filtering a noisy input comprised of an information-bearing signal and a noise part where no prior time domain value information or frequency domain parameter value information on the information bearing signal or noise is available and where no separate access to the information bearing signal or to the noise exists, the system comprising:

• (a) a spectrum shaping whitening filter responsive to the noisy input for rendering the noise part of the noisy input to become substantially white noise of a flat spectrum over the spectral range of interest and to provide a time domain output;
• (b) means for Fourier transforming the time domain output over successive finite frames of time to provide an amplitude spectrum output and a phase output;
• (c) a multiplier for providing a power spectrum output responsive to the amplitude spectrum output;
• (d) means for providing a zero mean power spectrum output responsive to the power spectrum output;
• (e) means for applying an inverse function of the multiplier to provide a resultant output;
• (f) means for inverse Fourier transforming the resultant output to provide a time domain resultant output;
• and
• (g) an inverse whitening filter, responsive to the time domain resultant output, for providing a substantially noise-free final output wherein the spectrum of the information bearing signal is unchanged and wherein the noise has been first whitened and then removed.

A method to filter inaccessible and unknown noise of arbitrary parameters from a noisy input, comprised of an information-bearing signal combined with a noise part, where no prior time domain parameters value or frequency spectrum domain parameters value on the information-bearing signal or the noise is available and where no separate access to the information-bearing signal or to the noise exists, the method comprising the steps of:

• passing the noisy input through a whitening filter to render the noise part of the noisy input to become substantially white noise of a flat power spectrum over the spectral range of interest to provide a time domain output;
• passing the time domain output through a white noise removal stage where the time domain output is Fourier transformed over successive finite frames of time to yield the time domain output's power spectrum of the output of the whitening filter and the time domain output's frequency spectrum;
• spectrally filtering the power spectrum by subtracting the d.c. average of the power spectrum from the power spectrum;
• inverse Fourier transforming the results of the spectral filtering the frequency spectrum to provide a resultant time domain output;
• and
• passing the resultant time domain output through an inverse whitening filter, which is the inverse of the whitening filter used prior to the Fourier transform, to provide a substantially noise-free output.

A system for filtering inaccessible and unknown noise of arbitrary parameters from a noisy input, comprised of an information-bearing signal combined with a noise part, where no prior time domain parameters value or frequency domain parameters value on the information-bearing signal or the unknown noise is available and where no separate access to the information-bearing signal or to the unknown noise exists, the system comprising:

• means for passing the noisy input through a whitening filter to render the noise part of the noisy input to become substantially white noise of a flat power spectrum over the spectral range of interest to provide a time domain output;
• means for passing the time domain output through a white noise removal stage where the time domain output is Fourier transformed over successive finite frames of time to yield the time domain output's power spectrum of the output of the whitening filter and the time domain output's frequency spectrum;
• means for spectrally filtering the power spectrum by subtracting the d.c. average of the power spectrum from the power spectrum;
• means for inverse Fourier transforming the results of the spectral filtering the frequency spectrum to provide a resultant time domain;
• and
• means for passing the resultant time domain output through an inverse whitening filter, which is the inverse of the whitening filter used prior to the Fourier transform, to provide a substantially noise-free output.