This invention relates to methods for processing noisy sound signals, especially for nonlinear noise reduction in voice signals, for nonlinear isolation of power and noise signals, and for using nonlinear time series analysis based on the concept of low-order deterministic chaos. The invention also concerns an apparatus for implementing the method and use thereof.
Noise reduction in the recording, storage, transmission or reproduction of human speech is of considerable technical relevance. Noise can appear as pure measuring inaccuracy, e.g., in the form of the digital error in output of sound levels, as noise in the transmission channel, or as dynamic noise through coupling of the system observed with the outside world. Examples of noise reduction in human speech are known from telecommunications, from automatic speech recognition, or from the use of electronic hearing aids. The problem of noise reduction does not only appear with human speech, but also with other kinds of sound signals, and not only with stochastic noise, but also in all forms of extraneous noise superimposed on a sound signal. There is, therefore, interest in a signal processing method by which strongly aperiodic and non-stationary sound signals can be analyzed, manipulated or isolated in terms of power and noise components.
A typical approach to noise reduction, i.e. to breaking down a signal into certain power and noise components, is based on signal filtering in the frequency band. In the simplest case, filtering is by bandpass filters, resulting in the following problem however. Stochastic noise is usually broadband (frequently so-called xe2x80x9cwhite noisexe2x80x9d). But if the power signal itself is strongly aperiodic and thus broadband, the frequency filter also destroys a power signal component, meaning inadequate results are obtained. If high-frequency noise is to be eliminated from human speech by a lowpass filter in voice transmission, for example, the voice signal will be distorted.
Another generally familiar approach to noise reduction consists of noise compensation in sound recordings. Here, for example, human speech superimposed with a noise level in a room is recorded by a first microphone, and a sound signal essentially representing the noise level by a second microphone. A compensation signal is derived from the measured signal of the second microphone that, when superimposed with the measured signal of the first microphone, compensates for the noise from the surrounding space. This technique is disadvantageous because of the relatively large equipment outlay (use of special microphones with a directional characteristic) and the restricted field of use, e.g., in speech recording.
Methods are also known for nonlinear time series analysis based on the concept of low-order deterministic chaos. Complex, dynamic response plays an important role in virtually all areas of our daily surroundings, and in many fields of science and technology, e.g., when processes in medicine, economics, signal engineering or meteorology produce aperiodic signals that are difficult to predict and often also difficult to classify. Thus, time series analysis is a basic approach for learning as much as possible about the properties or the state of a system from observed data. Known methods of analysis for understanding aperiodic signals are described, for example, by H. Kantz et al. in xe2x80x9cNonlinear Time Series Analysisxe2x80x9d, Cambridge University Press, Cambridge 1997, and H.D.I. Abarbanel in xe2x80x9cAnalysis of Observed Chaotic dataxe2x80x9d, Springer, N.Y. 1996. These methods are based on the concept of deterministic chaos. Deterministic chaos means that, although a system state at a certain time uniquely defines the system state at any random later point in time, the system is nevertheless unpredictable for a longer time. This results from the fact that the current system state is detected with an unavoidable error, the effect of which increases exponentially depending on the equation of motion of the system, so that after a relatively short time a simulated model state no longer bears any similarity with the real state of the system.
Methods of noise suppression were developed for time series of deterministic chaotic systems that make no separation in the frequency band but resort explicitly to the deterministic structure of the signal. Such methods are described, for example, by P. Grassberger et al. in xe2x80x9cCHAOSxe2x80x9d, vol. 3, 1993, p 127, by H. Kantz et al. (see above), and by E. J. Kostelich et al. in xe2x80x9cPhys. Rev. Exe2x80x9d, vol. 48, 1993, p 1752. The principle of noise suppression for deterministic systems is described below with reference to FIGS. 10a-c. 
FIGS. 10a-c show schematically the dependence of successive time series values for noise-free and noisy systems (exemplified by a one-dimensional relationship). The noise-free data of a deterministic system produce the picture shown in FIG. 10a. There is an exact (here one-dimensional) deterministic relationship between one value and the sequential value. The time delay vectors, details of which are explained further below, lie in a low-dimensional manifold in the embedding space. Upon introduction of noise, the deterministic relationship is replaced by an approximative relationship. The data are no longer on the low-dimensional manifold but close to it as shown in FIG. 10b. The distinction between power and noise is by dimensionality. Everything leading out of the manifold can be traced to the effect of the noise.
Consequently, the noise suppression for deterministically chaotic signals is made in three steps. First the dimension m of the embedding space is estimated and the dimension Q of the manifold in which the non-noisy data would be. For the actual correction, the manifold is identified in the vicinity of every single point, and finally the observed point is projected to the manifold for noise reduction as shown in FIG. 10c. 
The disadvantage of the illustrated noise suppression is its restriction to deterministic systems. In a non-deterministic system, i.e., in which there is no unique relationship between one state and a sequential state, the concept of identifying a smooth manifold, as shown in FIGS. 10a-c, is not applicable. Thus, for example, the signal amplitudes of speech signals form time series that are unpredictable and correspond to the time series of non-deterministic systems.
The applicability of conventional, nonlinear noise reduction to speech signals has been out of the question to date, especially for the following reasons. Human speech (but also other sound signals of natural or synthetic origin) is very much non-stationary as a rule. Speech is composed of a concatenation of phonemes. The phonemes are constantly alternating, so the sound volume range is changing all the time. Thus, sibilants contain primarily high frequencies and vowels low frequencies. So, to describe speech, equations of motion would be necessary that constantly change in time. But the existence of a uniform equation of motion is the requirement for the concept of noise suppression described with reference to FIGS. 10a-c. 
It is accordingly an object of the invention to achieve an improved signal processing method for sound signals, especially for noisy speech signals, by which effective and fast isolation of the power and noise components of the observed sound signal can be performed with as little distortion as possible.
It is also an object of the invention to provide an apparatus for implementing a method of this kind.
A first aspect of the invention consists, in particular, in recording non-stationary sound signals, composed of power and noise components, at such a fast sampling rate that signal profiles within the observed sound signal contain sufficient redundancy for the noise reduction. Phonemes consist of a sequence of virtually periodic repetitions (forming the redundancy). The terms periodic and virtually periodic repetition are set forth in detail below. In what follows, uniform use will be made of the term virtually periodic signal profile. The recorded time series of sound signals produce waveforms that repeat at least over certain segments of the sound signal and allow application, on restricted time intervals, of the above mentioned, familiar concept per se of nonlinear noise reduction.
According to another aspect of the invention, virtually periodic signal profiles are detected within an observed sound signal and correlations are determined between the signal profiles so that correlated signal components can be allocated to a power component and uncorrelated signal components to a noise component of the sound signal.
Yet another aspect of the invention is the replacement of temporal correlations by geometric correlations in the time delay embedding space, expressed by neighborhoods in this space. Points in these neighborhoods yield the information necessary for nonlinear noise reduction of the point for which the neighborhood is constructed.
Another aspect of the invention provides an apparatus for processing sound signals comprising a sampling circuit for signal detection, a computing circuit for signal processing, and a unit for the output of time series devoid of noise.