EP0518742B1 - Method for detecting a noisy wanted signal - Google Patents

Description

The present invention relates to a method of detection of a noisy useful signal.

One of the important problems in signal processing, simple as for its statement, but all the more complex as for its resolution, is to determine the presence or absence of a useful signal drowned in additive noise.

Various solutions are possible. We can use as variable the instantaneous amplitude of the signal received or processed by reference to a threshold determined experimentally.

We can also use the energy of the total signal over a time slot of duration T, by thresholding, always experimentally, this energy.

These thresholds allow a first presumption on the presence or absence of the signal. They are also applicable at any signal. Also, are they supplemented by "confirmation", defining "almost certain" criteria, specific to the type of useful signal, when the nature thereof is known a priori.

Such a complementary system is widely used in speech processing and can consist, for example, of a pitch extraction or minimum energy evaluation a vowel.

The subject of the present invention is a method of detection of a noisy useful signal, determining in the most rigorous possible the detection threshold, and able to work self-adaptively.

According to the invention, the signal / noise ratio is available expected signal to be processed, and we have a noise measurement only estimate, measurement digitized on M points, this noise being white or rendered white, we calculate an estimate of the average noise energy on these M points, we take a slice of N noisy signal points, we calculate an estimate of the average energy of these N points, we calculate a detection threshold different from 1 from the expected signal / noise ratio; we calculates the ratio of the two so-called estimated average energies, we compare this ratio to said threshold, and if this ratio is greater than the threshold, we decides on the presence of a useful signal, and if it is below this threshold, we decides that there is no useful signal.

The present invention will be better understood on reading the detailed description of an embodiment taken as an example not limiting.

We will first explain how to do it theoretically, in the ideal case, the detection of a noisy signal.

We have a first piece of information u (n) for a first time slot such as: u (n) = s (n) + x (n) n being an integer: 0 ≤ n ≤ N-1, s (n) being a useful signal and x (n) a noise. In addition, there is other information y (n), with 0 ≤ n ≤ M-1, and M can be equal to or different from this. y (n) is a measure of the noise x (n) over another time slot free of useful signal.

We ask: U = (u (0) 2 + u (1) 2 + ... + u (N) 2 )/NOT and V = (y (0) 2 + y (1) 2 + ... + y (M) 2 ) / M and Z = U / V

Thus, in an ideal and unrealistic case, we would have, by noting RSB = signal to noise ratio: Z = 1 + RSB and the simple detection criterion would be:
Z> 1: presence of useful signal
Z <1: absence of useful signal

According to the present invention, the theoretical threshold of 1 is replaced by a threshold µ, calculated as explained below, which takes into account the fact that the signals available are not perfectly ergodic and that U and V are only estimates of the true values of the variances σ _u 2 and σ _x 2.

To perform this calculation of µ, we proceed as follows next.

We start from the fact that the variables U and V are of a nature random, and therefore Z too. We then calculate the probability density of Z (which depends on the signal to noise).

Then, using the principle of maximum likelihood, determine the best estimate the signal-to-noise ratio after calculating the variable Z.

For this purpose, we measure over a time slice the variable U (n) above, and we measure the variable y (n) on a other time slice where we are sure that there is no useful signal, but only noise (independent and uncorrelated from s (n)).

To determine the density of the random variable Z (which can be called the observed variable), we proceed as follows. Let X ₁ belonging to N (m ₁ ; σ ₁ ² ) and X ₂ belong to N (m ₂ ; σ ₂ ² ) two independent Gaussian random variables for which the probabilities P _r {X ₁ <o} and P _r {X ₂ <o} are practically zero.

We ask: m = m 1 / m 2 , σ 2 = σ 1 2 / σ 2 2 , α = m 2 / σ 2 .

The probability density f _x (x) of X is then: f x (x) = -1/2 1 2π mx + σ 2 (x 2 + σ 2 ) 3/2 . e - α 2 2 . (x - m) 2 x 2 + σ 2 . U (x) where U (x) = 1 if x ≥ o and U (x) = o if x <o.

Yes h (x) = α. x - m (x 2 + σ 2 ) 1/2 we have: P (x) = P _r {X <x} = F [h (x)], expression in which F (x) denotes the characteristic function of the normalized Gaussian variable.

We now assume that the signals s (n), x (n) and y (n) are white, Gaussian and centered.

We pose

This last term is therefore also white, Gaussian and centered;
and we ask

Z est donc le rapport de deux variables gaussiennes indépendantes. On peut facilement démontrer que U et V sont indépendantes.Since we define σ _s ² and σ _x ² , we implicitly assume that the probability density is calculated at σ _s ² and σ _x ² known. We therefore evaluate the density of Z by knowing σ _s ² and σ _x ² . In this case, U and V follow laws of chi-2, and, for N and M sufficiently large, U and V are approximated by Gaussian laws practically always positive:
U belongs to

Z is therefore the ratio of two independent Gaussian variables. We can easily demonstrate that U and V are independent.

With: m ₁ = σ _u ² , σ ₁ ² = 2σ _u ⁴ / N, m ₂ = σ _x ² , σ ₂ ² = 2σ _x ⁴ / M
it comes: m = σ _u ² / σ _x ² , σ ² = (M / N) (σ _u ² / σ _x ² ) ² , α = (M / 2) ^1/2 .
Now: σ _u ² / σ _x ² = 1+ r where r = σ _s ² / σ _x ² is the signal to noise ratio. Let k = M / N, it comes: m = r + 1, σ ² = k (r + 1) ² .

1°) x ≥ 0 fz(z:σs 2, σx 2) = (M/4π)1/2 (r+1) z+k(1+r)[z2+k(r+1)2]3/2 e - M[z-(r+1)]2 4[z2+k(r+1)2]

2°) x ≤ 0 d'où : f_z(z : σ_s ², σ_x ²) = 0

The probability density of Z, knowing σ _s ² and σ _x ² , is therefore expressed by:

1 °) x ≥ 0 f z (z: σ s 2 , σ x 2 ) = (M / 4π) 1/2 (r + 1) z + k (1 + r) [z 2 + k (r + 1) 2 ] 3/2 e - M [z- (r + 1)] 2 4 [z 2 + k (r + 1) 2 ]

2 °) x ≤ 0 where: f _z (z: σ _s ² , σ _x ² ) = 0

We will ask: f k, M (z, r) = (M / 4π) 1/2 (r + 1) z + k (1 + r) [z 2 + k (r + 1) 2 ] 3/2 e - M [z- (r + 1)] 2 4 [z 2 + k (r + 1) 2 ] U (z) so that: f _z (z: σ _s ² , σ _x ² ) = f _{k, M} (z, σ _s ² / σ _x ² )

From the above results relating to the probability density f _x (x), we deduce the probability Pr {Z <z: σ s 2 , σ x 2 }.

Is : h kM (x, r) = (M / 2) 1/2 x - (r + 1) [x 2 + k (r + 1) 2 ] 1/2 It comes: Pr {Z <z: σ _s ² ; σ _x ² } = F {h _{k, M} (x, r)}.

We will now examine the case of any signal s (n) and a white Gaussian noise.

We always assume that the noises x (n) and y (n) are white, Gaussian with σ _x ² = E [x (n) ² ] = E [y (n) ² ]. The useful signal s (n) is assumed to be arbitrary, independent of noise.

The new hypothesis made here is to assume that s (n) and x (n) are uncorrelated in the temporal sense of the term, that is to say: c = Σ 0 ≤ n ≤ N-1 s (n) x (n) (Σ 0 ≤ n ≤ N-1 s (n) 2 ) 1/2 (Σ 0 ≤ n ≤ N-1 x (n) 2 ) 1/2 = 0

We then show that U can be approximated by: U = µ 2 s + (1 / N) Σ 0 ≤ n ≤ N-1 x (n) 2 and Z by: Z = µ s 2 + (1 / N) Σ 0 ≤ n ≤ N-1 x (n) 2 (1 / M) Σ 0 ≤ n ≤ M-1 y (n) 2

As above, the calculation of the density of Z was done by knowing σ _s ² and σ _x ² , here the calculation will be done by knowing µ _s ² and σ _x ² . The density to be calculated will be noted by f _z (z: µ 2 / s, σ 2 / x).

(µ_s ² + σ_x ²; (2/N) σ_x ⁴). V appartient à (σ_x ² ; (2/M) σ_x ⁴).Knowing µ _s ² , U = µ _s ² + (1 / N) Σ 0≤n ≤ N-1 x (n) ² belongs to

(µ _s ² + σ _x ² ; (2 / N) σ _x ⁴ ). V belongs to (σ _x ² ; (2 / M) σ _x ⁴ ).

Z = U / V is therefore approximated by the ratio of two independent Gaussian laws. As U and V are independent, we therefore apply the result concerning the probability density of X, with: m 1 = µ s 2 + σ x 2 , σ 1 2 = (2 / N) σ x 4 , m 2 = σ x 2 , σ 2 2 = (2 / M) σ x 4 So: m = r + 1, σ ² = k, α = (M / 2) ^1/2 , with k = M / N and r = µ _s ² / σ _x ² .

The probability density of Z, knowing µ _s ² and σ _x ² is therefore equal to: f z (z: µ s 2 , σ x 2 ) = (M / 4π) 1/2 (1 + r) z + k [z 2 + k] 3/2 e - M 4 [z- (r + 1)] 2 z 2 + k . U (z) We will ask: f k, M (z) = (M / 4π) 1/2 (1 + r) z + k [z 2 + k] 3/2 e - M 4 [z- (r + 1)] 2 z 2 + k . U (z) so that: f _z (z: σ _s ² , σ _x ² ) = f _{k, M} (z, σ _s ² / σ _x ² )

From the above results concerning the probability density of X, we deduce the probability Pr {Z <z: µ s 2 , σ x 2 }. Is: h k, M (x, r) = (M / 2) 1/2 x - (r + 1) [x 2 + k] 1/2 it comes: Pr {Z <z: µ _s , σ _x ² } = F (h _{k, M} (x, r))

According to the present invention, the activity detection using a maximum of likelihood.

In the case of processed signals, the probability density of the variable Z, knowing the energies of the useful signal and of the noise, is expressed by a function of the form:
f _{k, M} (z, r) where r denotes the signal to noise ratio. This probability therefore depends on the signal to noise ratio. Also, the decision rule can only be given with an expected signal-to-noise ratio. Let r _{o be} this expected signal-to-noise ratio.

We assume that the probability of the absence of s (n) is π _o and that the probability of the presence of s (n) is π ₁ .

Since we know the probability density f _{k, M} (z, r) the optimal decision rule is provided by the general theory of detection and is expressed by: π 1 f k, M (z, r o ) π o f k, M (z, 0) > 1 ⇒ D = 1 π 1 f k, M (z, r o ) π o f k, M (z, 0) <1 ⇒ D = 0

We can also express this decision rule in the form: (Z <µ ⇒ D = 0) and (Z> µ ⇒ D = 1).

We must then determine µ and solve the equation: ln [f k, M (z, r o )] - ln [f k, M (z, 0)] - ln (π o / π 1 ) = 0.

We then demonstrate that the probability of error is worth: Pe = π o [1 - F (h k, M (µ, 0))] + π 1 F H k, M (µ, r o )).

We will now examine the case of the detection of a white Gaussian signal in a white Gaussian noise itself.

The signals s (n), x (n) and y (n) are assumed to be white, Gaussian, centered. Let r _{o be} the expected signal-to-noise ratio, and k = M / N. the probability of absence of s (n) is π _o and the probability of presence of s (n) is π ₁ .

Décision D = 1 lorsque :

Décision D = 0 lorsque :

The decision rule is then:

Decision D = 1 when:

Decision D = 0 when:

The threshold being determined for equality (instead of inequality) between the terms of these two expressions.

We can also express this decision rule in the form: (Z <µ ⇒ D = 0) and (Z> µ ⇒ D = 1).
We obtain for example for µ, at M = N = 128, π _o = π ₁ = 1/2: r _o in dB µ -2 1.27 -1 1.34 0 1.41 1 1.50 2 1.68

The probability of error is: Pe = π o [1-F (h k, M (µ, 0))] + π 1 F H k, M (µ, r o ))) with: h k, M (x, r o ) = (M / 2) 1/2 x - (r o +1) [x 2 + k (r o +1) 2 ] 1/2

We give below some values of Pe as a function of r _o . π _o and π ₁ are taken equal to 0.5. r _o in dB Pe -2 0.086 -1 0.052 0 0.028 1 0.013 2 0.005

In a simulation example, a white Gaussian noise with unit variance was generated. For each frame of 128 points (N = M = 128), it was randomly decided to generate an additive noise s (n), having a signal to noise ratio defined beforehand. The probability of appearance and absence (π _o and π ₁ ) is equal to 0.5. We generated a second Gaussian white noise of unit variance, which was used to calculate the random variable V. For each frame, we calculated Z. We then applied the decision rule and we counted the number of errors . r _o in dB Number of errors in 1000 iterations -2 73 -1 43 0 18 1 10 2 2

These results corroborate those predicted by the calculation theoretical.

We will now examine the case of any signal s (n) and a white Gaussian noise.

Décision D = 1 lorsque : ln (ro+1) z+kz+k > (M/4) [z-(ro+1)]2 - (z-1)2 z2+k + ln πo π1

Décision D = 0 lorsque : ln (ro+1) z+kz+k < (M/4) [z-(ro+1)]2 - (z-1)2 z2+k + ln πo π1

We always assume that the noises x (n) and y (n) are white, Gaussian with σ _x ² = E [x (n) ² ) = E (y (n) ² ]. The useful signal s (n) is assumed to be arbitrary, independent of noise. Let r _{o be} the expected signal-to-noise ratio, k = M / N. The probability of absence of s (n) is π _o and that of the presence of s (n) is π ₁ .
The decision rule is then:

Decision D = 1 when: ln (r o +1) z + k z + k > (M / 4) [z- (r o +1)] 2 - (z-1) 2 z 2 + k + ln π o π 1

Decision D = 0 when: ln (r o +1) z + k z + k <(M / 4) [z- (r o +1)] 2 - (z-1) 2 z 2 + k + ln π o π 1

We can also express this decision rule under the form: (Z <µ ⇒ D = 0) and (Z> µ ⇒ D = 1).

The following values are obtained for p as a function of r _o , for M = N = 128, π _o = π ₁ = 1/2. r _o in dB µ -2 1.30 -1 1.38 0 1.48 1 1.60 2 1.76

In addition, we get: Pe = π o [1-F (h k, M (µ, 0))] + π 1 F H k, M (µ, r o ))) with: h k, M (x, r o ) = (M / 2) 1/2 x - (r o +1) [x 2 + k] 1/2

We give below some values of Pe as a function of r _o . The probabilities π _o and π _o are taken equal to 0.5. r _o in dB Pe -2 0.062 -1 0.032 0 0.013 1 0.004 2 0.001

In a simulation example, for each frame of 128 points of white noise generated (N = M = 128), we decided randomly to add s (n), which is here, a sinusoid, presenting a signal to noise ratio defined beforehand. π ₁ and π _o are taken equal to 0.5.

We generated a second Gaussian white noise of variance unit, used to calculate V. For each frame, Z and the above decision rule was applied. We counted the number of errors.

The following results were obtained: r _o in dB Number of errors in 1000 iterations -2 70 -1 37 0 12 1 6 2 3

These results corroborate those predicted by the calculation theoretical.

The previous results, because very general, allow the detection of signals embedded in additive noise, even when the signal to noise ratio is low, close to 0 dB.

We will describe below an application in which this type of detection can be very useful.

The algorithms presented apply to the case of speech, as a voice activity pre-system.

The choice of detection threshold depends on the context.

Regarding the audio tapes used, a noise and speech characterization, using measures based on maximum likelihood estimation shows that the voice signal to be detected has a signal ratio on noise of at least 6 dB.

On the other hand, the processing system uses 128-point signal frames, the sampling frequency being 10 kHz.

The variables U and V are both evaluated on 128 points so that M = N = 128.

From the above, we deduce the theoretical threshold of detection at 3.

However, we cannot be satisfied with this unique threshold. Indeed, if the noise is relatively stationary, it presents instabilities to take into account to renew the variable V, which makes the algorithm partially adaptive.

We therefore introduce a second threshold, which allows decide whether the variable V will be renewed or not.

This second threshold is chosen at 1.25, which corresponds to additive noise to stationary noise with a ratio signal to noise of -2 dB.

Si Z < 1,25 : Alors la trame traitée est composée du même bruit que celle utilisée comme référence. La variable V est remplacée par la valeur de l'énergie de la trame traitée.On notera que, puisque la décision est de considérer la trame traitée comme du bruit représentatif, on pourrait renouveler la variable V en faisant la moyenne de l'ancienne valeur de V et de l'énergie de la trame considérée. Ce qui amène à changer la valeur de M (nombre de points sur lequel est évalué V) mais cette opération peut induire un mauvais fonctionnement de l'algorithme.

Si 1,25 < z > 3 : La trame est considérée comme contenant une non-stationnarité du bruit, et exempte de parole.

Si 3 < Z : La trame est considéré comme de la parole.

The decision rule is then:

If Z <1.25 : Then the processed frame is composed of the same noise as that used as a reference. The variable V is replaced by the value of the energy of the processed frame. Note that, since the decision is to consider the processed frame as representative noise, we could renew the variable V by averaging the old value of V and of the energy of the frame considered. This leads to changing the value of M (number of points on which V is evaluated) but this operation can induce a malfunction of the algorithm.

If 1.25 <z> 3 : The frame is considered to contain noise non-stationarity, and free of speech.

If 3 <Z : The frame is considered to be speech.

Tests carried out on signal samples noises validated this detection.

However, remember that this voice detection can be improved by the use of signal specific criteria speech, such as calculating pitch.

The algorithm proposed here concerns the study of some examples of signals. It is obvious that for other signals of speech with different signal-to-noise ratios, a new choice of thresholds is necessary.

The use of two thresholds is generally preferable.

An application of this algorithm makes it possible to create correct reference files for the recognition system vocal studied. A precise segmentation of speech is then necessary.

In one application, we used a micro switch (micro opening and closing) which provides segmentation coarse speeches.

The previous algorithm was used to refine this work-study program. A first pass of the algorithm made it possible to specify the start of speech. A second pass consisted in reading the speech file "upside down", that is to say starting from the microphone closure to microphone opening. This then made it possible to specify the end of the speech.

This non-causal use of the algorithm is necessary because the activity detection is sufficiently precise to detect, within words, the presence of silences, which is detrimental to the implementation of segmentation for learning.

The same type of application also allows to segment speech files on which we perform a recognition.

However, this algorithm is obviously not causal, which is detrimental to real time use. Hence the need to complete this algorithm with a calculation specific to speech processing.

We have demonstrated the existence of optimal thresholds of detection, which provides a theoretical approach to the problem of estimating the signal to noise ratio and, above all detection, in the case of white noise and a signal known only by its energy on N points when it remains relatively stationary.

Claims (5)

1. Method of detecting a useful signal affected by noise, for which the expected signal/noise ratio of the signal to be processed is available, and a measurement of the estimated noise alone is available, a measurement enumerated over M points, characterized in that an estimate of the mean energy of the noise over these M points (V) is calculated, a slice of M points of noise-affected signal is taken, an estimate of the mean energy of these N points (V) is calculated, a detection threshold (µ), differing from 1, is calculated on the basis of the expected signal/noise ratio (r_o), the ratio (Z) of the two said estimated mean energies is calculated, this ratio is compared with the said threshold, and, if this ratio is above the threshold, it is decided that a useful signal is present, and, if it is below this threshold, it is decided that a useful signal is absent.
2. Method according to Claim 1, characterized in that the estimated noise alone is white or made to be white.
3. Method according to one of the preceding claims, in the case where the useful signal is any signal and the noise is a gaussian white noise, characterized in that the theoretical detection threshold is the solution for Z = µ of the following equation: ln (ro+1)z+kz+k = (M/4) [z-(ro+1)]2 - (z-1)2 z2+k + ln πo π1 r_o being the expected signal-to-noise ratio, k = M/N, π_o being the probability of absence of the useful signal and π₁ its probability of presence.
4. Method according to one of Claims 1 or 2 for detection of a gaussian white signal affected by noise which is also white and gaussian, characterized in that the theoretical detection threshold is the solution for Z = µ of the following equation:

   

   r_o being the expected signal-to-noise ratio, k = M/N, π_o being the probability of absence of the useful signal and π₁ its probability of presence.
5. Method according to one of Claims 1 to 3, for speech detection, characterized in that over and above the theoretical detection threshold a second decision threshold is used for updating the measured slice of the estimated noise alone, in order to take account of non-stationary noise.