WO2002093553A1

WO2002093553A1 - Estimation of fundamental periods of multiple concurrent sources in particular of sound

Info

Publication number: WO2002093553A1
Application number: PCT/FR2002/001628
Authority: WO
Inventors: Alain De Cheveigne
Original assignee: France Telecom
Priority date: 2001-05-17
Filing date: 2002-05-15
Publication date: 2002-11-21
Also published as: FR2824932A1; FR2824932B1

Abstract

For several variables of fundamental periods (t1, t2) of a digital signal, for example a sound signal, included in the variation intervals (T1min, T1max, T2min, T2max), a linear combination (Dn) of values of the autocorrelation function (rn(t)) for at least one sample (x(n)) of the digital signal is determined. A combination of minimum value is sought (E2) to produce rapidly (E3) the variables of the periods for said combination as estimated periods (T1, T2). The values of the autocorrelation function assessed in the linear combination can be respectively weighted by amplitude variations of component signals having said fundamental periods (T1, T2) which are likewise estimated.

Description

Estimation of fundamental periods of multiple concurrent sources including sound

The present invention relates to an estimation of fundamental periods of multiple concurrent sources.

The fundamental frequency, or its inverse, the fundamental period, is a useful parameter for determining the intonation of a speech signal, and the perceived pitch of a musical sound. In some applications, it often happens that musical instruments play together, or that several speakers speak at the same time, which makes it difficult to estimate the fundamental frequencies of individual voices. However, the estimation of these fundamental frequencies is all the more useful since they constitute parameters used in sound source separation procedures, and in models of auditory scene analysis.

Various methods have been proposed for the estimation of fundamental frequencies of isolated periodic signals, such as the notes of an instrument or the voiced parts of a speaker's speech. The estimates resulting from these methods are not satisfactory, even for isolated sounds, but are reliable in many cases. On the other hand, most of the methods fail as soon as several sounds are mixed, because the hypothesis of periodicity of the signal which they require is no longer verified.

In particular, the article "Multiple period estimation and pitch perception model" by Alain de Cheveigné and Hideki Kawahara, Speech Communication 27 (1999), p. 175-185 suggests replacing the classical search for a maximum of functions autocorrelation of the digital signal to be processed to estimate fundamental frequencies thereof, by searching for a minimum of a sum function squared of differences in the signal, through a cascade of filters allocated respectively to the periods to be estimated . However, this article does not address the economic aspect of such research which is all the longer the greater the number of periods to be estimated.

The present invention aims to provide a method for estimating fundamental periods of sound sources based on minimizing differences in the signal to be processed, while reducing the iterations and operations intrinsic to the estimation so that the estimation is quick and free. the signal processing means in which the method is implemented for other tasks.

To this end, the method for estimating several fundamental periods of a digital signal in a signal processing means, according to which the autocorrelation function for at least one sample of the digital signal is previously evaluated for predetermined variables of the periods included in predetermined intervals of variation of the fundamental periods, is characterized in that it comprises a determination of a linear combination of values of the autocorrelation function evaluated for zero, of the respective variables of periods and of the sums and partial differences of these ci, and a search for a combination of minimum value among the determined combinations in order to produce the variables respective periods for this minimum value combination as estimated periods.

In order to further reduce the duration of the estimation of the periods, the prior evaluation of predetermined terms of the autocorrelation function r _n (t) for the sample n and the variable t can be followed by a prior evaluation of terms predetermined from the following difference function: d _n (t) = r _n (0) + r _{n + t} (0) - 2r _n (t) in order to evaluate said linear combination as a function in particular of values of the difference function .

For another embodiment of the method of the invention, the signal is modeled as a sum of periodic functions which can have amplitudes which vary slowly. The method provides estimates of the fundamental periods, or frequencies, of each source, and also, for sources whose amplitude is not constant, estimates of their amplitudes or rates of change in amplitude over time.

To this end, the method is characterized in that, when the digital signal is assumed to result from component signals having respectively said fundamental periods and amplitude variations during said periods, the values of the autocorrelation function evaluated for respective variables of periods and partial sums and differences of these in the linear combination are weighted respectively by one of the amplitude variations, of the squares of these and of the products of these, after estimation of the amplitude variations . More particularly, the fundamental periods are first estimated by supposing that the amplitudes do not vary, then each variation in amplitude is estimated by canceling the derivative of said linear combination weighted with respect to the variation in amplitude and evaluating said variation amplitude variation for values of the autocorrelation function corresponding to the periods estimated and weighted by the amplitude variations already estimated, and finally by another estimation of the fundamental periods by evaluation of the weighted linear combination with the variations in amplitude estimated.

The duration of the search can be reduced when it consists in finding a first minimum value among combinations determined for the variation interval relating to a first period and predetermined constant values of the other periods, then a second minimum value among combinations determined for the first minimum value and the variation interval relative to a second period and predetermined constant values for the other periods, and so on until a minimum value of the linear combination is obtained which is less than a predetermined threshold, or up to to meet any other criteria for terminating the search.

Other characteristics and advantages of the present invention will appear more clearly on reading the following description of several preferred embodiments of the invention with reference to the corresponding appended drawings in which: - Figure 1 is a schematic block diagram of a signal processing means for the implementation of the estimation method according to the invention; and

- Figure 2 is an algorithm for estimating fundamental periods of a signal entering the processing means, according to the method of the invention.

With reference to FIG. 1, an analog analog input signal x, such as a sound signal from an auditory scene or a musical piece, is sampled at sampling instants 1, ... n, ... N in an analog-to-digital converter 1 to a digital sample signal x (n) which is applied to a signal processing circuit 2 to estimate fundamental periods making up the incoming signal and / or amplitudes and / or periodicity measurements .

The sampling period in the converter 1 is theoretically set equal to a time unit in order to simplify the writing of the relationships in the following description.

The number P of estimated periods may be known in advance, or may itself be the subject of an estimate. The circuit 2 is for example the central processing unit of a computer connected to a non-volatile memory 3.

According to a first embodiment of the invention, it is assumed that the incoming signal x (n) is generally modeled as a sum of P periodic functions Xp (n) of constant amplitude and of respective periods T _p , with 1 <p <P and Tp -j_ _n <Tp <Tp _max , the product of the number of samples N by the sampling period being a priori greater than the sum of the maximum values Tp _max of the various periods Tp: p≈P x (n) = ∑ Xp (n). p = l

The current autocorrelation function r _n (t) of the signal x (n) of period variable t at the sampling instant n depends on the size W of an integration window expressed in number of samples according to the following relationship:

--n + W-1 r _n (t) = Σ x (i) x (i + t) ι = n

The autocorrelation function r _n (t) is said to be "current" since the calculation is repeated sample by sample by dragging the window for 1 <n <N with t + W -l ≤ N - n. The autocorrelation function is calculated for all the values of the period variable t comprised between a minimum value t _mn and a maximum value t _max which depend on the ranges of periods sought, and for any value of n such that 1 <n < N with t

+ - l ≤ N - n.

To quickly obtain the values of the autocorrelation function, the following operations are carried out for each value of t: i = W

- form the sum ri (t) = _J x (i) x (i + t); i = l

- for each value of n, 1 <n <N-W-t + 1, apply the recurrence relation:

r _n (t) = r _n -ι (t) -x (nl) x (n-l + t) + x (n + Wl) x (n + W + tl). These operations operate a smoothing of x (i) x (i + t) by convolution with a square window of size W. By applying these smoothing operations a second time to the autocorrelation function r _n (t), ie

i = n + Wl r _2n (t) = Σ r _n (t) /, i = n

we obtain a smoothing with a triangular window of size 2W-1. By repeating these operations, an increasingly rounded window is obtained, the shape of which approaches a Gaussian. The number of repetitions of these operations is at the discretion of the developer of the method according to the invention.

Other recurrence formulas make it possible to implement, by recurrence and with comparable efficiency, other forms of window for integrating the autocorrelation function.

The following current difference function d _n (t) expresses the difference of the digital signal x at an instant i and at a later instant i + t where t can denote a fundamental period sought:

i = n + Wl d _n (t) = ∑ (x (i) - x (i + t)). i = n

The difference function d _n (t) is calculated for the same range of parameters, and can undergo the same smoothing method as the current autocorrelation function r _n (t). The difference function can be expressed in dependence on the autocorrelation function: d _n (t) = r _n (0) + r _{n + t} (0) - 2r _n (t) in order to benefit from the recurrence relation and thus increase the speed of determining the difference function by precalculating linear combinations of r _n (t).

In the remainder of the description, the current autocorrelation function r _n (t) or the current difference function d _n (t) can be considered to be smoothed one or more times, if the smoothing has been used as a recurrence formula for implement the integration window.

The estimation method according to the invention i supplemented in circuit 2 comprises, after an initial step E0, essentially three main steps El, E2 and E3 shown in FIG. 2 and detailed below, according to a first variant of the first realization of the invention.

The incoming digital signal x (n) is assumed to result from the sum of P = 2 concurrent periodic sounds of periods T] _ and T ₂ and of constant amplitude. At the initial stage En, the developer has previously selected the limits of the variation intervals Tι _m _ _n <Ti <T _max and 2mi _n ≤ T ₂ ≤ T _2max of the two periods T] _ and T ₂ and has written them in memory 3. Circuit 2 writes N samples received x (l) to x (N) in memory 3.

Then in step E1, circuit 2 determines the sum rι (t), then all the values of the autocorrelation function r _n (t) and of the difference function d _n (t) for all the values 0, t] _, t ₂ , ti + t ₂ and t ₂ - t] _ of t included in the two period intervals T _lmin ≤ ti ≤ Tι _max and T _2min <t ₂ ≤ τ _2max .

If signal x looks like its model, the following double difference function for sample x (n): --n + W-

D _n (tι, t ₂ ) = Σ [(x (i) - (x (i + tι) - (x (i + t ₂ ) -x (i + tι + t ₂ ) in

must be zero when ti = 1 and t ₂ = T ₂ . Conversely, the double difference function can only be canceled if ti = Mι_Tι and t ₂ = M ₂ T with M] _ and M ₂ of integers. The processing circuit 2 then estimates in step E2 the periods T and T ₂ by determining the difference function D _n (tι, t ₂ ) for all the values of the periods ti and / or t ₂ in the variation intervals, by incrementing each variable ti and t ₂ by an increment Δt equal to the sampling period of the signal x (n) or to an integer multiple Δn thereof. At each incrementation of variable t] _, t ₂ , circuit 2 compares the difference D _n (tι, t ₂ ) with that previously calculated D _n -i and stores the smallest difference with the corresponding period values T] _ = ti and T ₂ = t. In the case where the minimum value of D _n (t_, t ₂ ) is reached for several pairs of periods, circuit 2 retains one, for example the one whose values are the lowest. Thus, circuit 2 searches for the minimum of D _n (tχ, t ₂ ) in the space with two parameters (ti, t ₂ ). This determination can be made exhaustively for all the pairs (t] _, t ₂ ) belonging to [Tι _min , Tι _max ] x [T _2min , T _2max ]. Preferably, circuit 2 does not determine the function D _n (tχ, t ₂ ) for the pairs (t] _, t ₂ ) for which the inverse pair (t ₂ , t) has already been determined, since D _n ( tι, t ₂ ) = D _n (t ₂ , ti) and r _{n + 1} ( ₂ -tι) = ^r n + t ₂ ^(t l ^"fc 2 ^{) •}

Circuit 2 does not estimate D _n (tι, t ₂ ) according to the previous relationship by determining all the doubles differences squared for each sample n for each value of i, to avoid too long a determination time. This time is reduced by developing the difference function with the autocorrelation function:

> n (ti, t ₂ ) = r _n (0) + r _{n + tl} (0) + r _{n + t2} (0) + _{n + tl +} t ₂ (<

- 2r _n (tι) - 2r _n (t ₂ ) + 2r _n (tι + t ₂ )

+ 2r _n + t _] _ ⁽ 2 ^~ ι) - 2r _{n + tl} (t) - 2r _{n +} t ₂ (tl ^'

The determination of D _n (tι, t ₂ ) amounts to calculating a linear combination of ten values of the current autocorrelation function for variables t respectively equal to zero, to respective variables of the periods and t ₂ and to sums and partial differences ti + t ₂ and t ₂ _ ti of these. Preferably, certain terms are grouped and replaced by values of the difference function d _n (t) to obtain for example the following relation:

D _n (tι, t ₂ ) = d _n (tχ) + d _{n + t2} (ti) - 2r _n (t ₂ ) + 2r _n (tι + t ₂ ) + 2r _{n + tl} (t ₂ -tι) - 2r _{n + tl} (t ₂ )

in order to further reduce the time for determining D _n (t] _, t ₂ ) to the sum of six terms instead of ten. This makes the process affordable, despite the size of the search space.

According to another variant, the exhaustive search for the minimum of the difference function D _n (t] _, t ₂ ) is replaced by another search strategy, for example iterative, in which only a subset of the set of pairs [Tι _m i _n , Tlmax] x [T _2m in T _2max ] is scanned. For example, the circuit 2 searches for a first minimum value D _n (t] _, t ₂ ) for the variation interval [Tι _m i _n , ^τ lmaχ] relative to one of the periods ti while maintaining constant at a given value t l ' other period; then for the period ti corresponding to this first minimum value, a second minimum value of D _n for the variation interval [T _m j_ _n , T _2max ] relative to the other period t while keeping the first period constant at the value previously estimated; then for the period t ₂ corresponding to this second minimum value of D _n , a third minimum value of D _n for the variation interval [ι _min , Tι _max ] and so on until a lower value of D _{n is} obtained at a predetermined tolerance level. This variant has the advantage of reducing the time for determining the minimum difference. The criterion for comparison with a predetermined threshold can be replaced by any other criterion for terminating the search. According to yet another variant, before looking for the minimum value, any transformation which favors certain estimates over others, as a function of their values, is applied to the function D _n (tι, t ₂ ) •

According to other variants, the above transformation, or the limits of the period search space, or the period values found, are dynamically adjusted as a function of results obtained beforehand for other positions in the signal, or based on other information.

According to another variant, interpolation techniques are applied to the function D _n (t] _, t ₂ ) to improve the resolution. A display 4 at the output of the signal processing circuit 2 indicates a pair of estimated periods T] _, T ₂ as indicated in a step E3. As a variant, circuit 2 also provides the display 4 with the following measurements which provide information on the degree of periodicity of the signal: ei = 2d _n (Tι) / [r _n (0) + r _{n + Tl} (0)] e ₂ = 2d _n (T ₂ ) / [r _n (0) + r _{n +} τ ₂ (0)] ei2 = 4 D _n (Tι, T ₂ ) / [r _n (0) + r _{n + Tl} (0) + r _{n + T} ; ₂ (0)

^{+ r} n + Tι + T ₂ ⁽ ° ^{)] •}

The values e_, e ₂ and eχ2 represent a proportion of residual energy when the periodic part of period of Ti, that of period T, or both is removed respectively.

The first embodiment of the invention is not limited to the estimation of two fundamental periods and relates more generally to the estimation of the fundamental frequencies of P competing signals of constant amplitude mixed in the incoming digital signal x (n).

According to this more general variant, it is assumed that the incoming signal x results from the sum of P concurrent periodic sounds of respective periods T] _, ... T _p ... Tp.

The signal processing circuit 2 cascaded filters the P variables of periods ti to tp. A first filter cancels the components in the signal x (n) relative to the variable of period t] _, that is:

i = n + W-l 2

D _n (tι) = ∑ (Xι (x (i))) i = l i≈ + W-1

! x (i) - x (i + tι) ι = n

then a second filter cancels the components relating to the variable of period t ₂ in the filtered residual signal, namely:

i = n + W-l 2

D _n (tι, t ₂ ) = ∑ (X ₂ (Xι (i))) i = ni = _n + Wl

Σ (Xl (i) - Xι (i + t ₂ )) in i = n + Wl Σ (x (i) -x (i + tι) -x (i + t ₂ ) + x (i + t + t ₂ ; ι = n

then a third filter cancels the components leaving the second filter and relating to the variable of period t ₃ , that is:

i≈n + W-1 ₂

D _n (tι, t ₂ , t ₃ ) = ∑ (X ₃ (X ₂ (i))) i = ni = n + Wl 2

∑ (X ₂ (Xι (i)) - (X ₂ (Xl (i + t ₃ ))) i = ni = n + Wl

Σ (x (i) -x (i + tι) -x (i + t ₂ ) + x (i + tι + t ₂ ) - i = n

2 i + tι + t ₂ + t3)); X (i + t3) + x (i + tι + t3) + x (i + t ₂ + t3) -x (0 and so on until a Pth filter which cancels the components relating to the variable of period tp , that is the order difference function P:

i = _n + W ~ l 5 D _n (tι, ... t _p , ... t _P ) = ∑ (Xp (X _P _ ₁ (... Xp (... X ₃ i = n

(X ₂ (Xl (i))) ...) ...)) ² , P which depends on an elevation squared of 2 terms of type x (i) with the recurrence formula

Xp (Xp-l (i)) = X _p -i (Xp- ₂ (i)) - Xp-i (Xp- ₂ (i + tp))

and which must be zero when tp = Tp for p = 1, ... P so that the responses of the P filters defined above are zero respectively for the values ti = Ti, ... tp = Tp. Conversely, the above difference function is zero only if tp = MpTp where Mp is an integer, for p = 1, ... P. The processing circuit 2 then estimates at a step analogous to step E2 the periods Ti, ... Tp by searching for the minimum of D _n (tι, ..., tp) in the space with P parameters (t] _, ..., tp).

As in the variant where P = 2, the expression of D _n (t] _, ..., tp) is developed into a sum of terms of the current autocorrelation function r _n (t), or a sum of terms of the current autocorrelation function r _n (t) and of the current difference function d _n (t).

The algorithm shown in Figure 2 for the variant P = 2 thus extends to any P. In the parameter space [T _lm i _n , Tι _max ] x ... [T _Pm i _n , Tp _max ], circuit 2 searches for the minimum of the function D _n (t] _ _Λ ..., tp ). Even more than in the case P = 2, the search to be precise must be exhaustive.

The estimation method according to the invention thus produces a set of P estimated periods. It can also provide measures of periodicity which serve as indicators of the reliability of the estimate. According to a second embodiment of the invention, it is assumed that each periodic function Xp (n) composing the incoming signal x (n) has an amplitude ap (n) which varies slowly and which satisfies the following relationship - over a respective period Tp for all 1 <n ≤ N-Tp:

Xp (n + T _p ) / a _p (n + Tp) = x _p (n) / a _p (n).

The model of the signal x (n) degenerates into a sum of periodic signals of constant amplitude according to the first embodiment, for a _p = 1, and into a single periodic sound for P = 1.

According to a simple variant of the second

15 embodiment, the digital signal to be processed x (n) results from the sum of two digital periodic sound signals xj_ and X2 having variable amplitudes of variation ai and a2 varying slowly during their respective periods T and T2, such as:

20 xi (n + T) = aixi (n) x ₂ (n + T ₂ ) = a2X ₂ (n). If either signal was isolated, the variation in amplitude of this signal could be compensated for by normalizing the signal before estimation. However, in

In general, the amplitudes of the two signals xi and x ₂ vary independently of one another. The algorithm shown in Figure 2 nevertheless adapts to this second embodiment.

If the signal matches its model, the

30 difference function of the sounds DA _n (tι, t ₂ ) for the sample x (n):

i = Wl DA _n (tι, t ₂ ) = ∑ [(x (i) -aιx (i + tι) - (a ₂ x (i + t ₂ ) -aιa ₂ x (i + tι + t ₂ )) ] i = ft must be zero when ti = Ti and t = T ₂ .

By developing the double difference function DA _n with the autocorrelation function r _n in a step analogous to step E2, the time for determining the function DA _n (tι, t2) is reduced in circuit 2:

+ senior _{n + tl} (0) + a2 ^r n + t ₂ ^{(0) +} senior _{n + tl + t2} (0; 2aιr _n (tι) 2a ₂ r _n (t ₂ ) + 2aιa2 _n (tι + t2) + 2aιa ₂ r _{n + tl} (t ₂ -tι) - aï 2r _{n + 1} (t ₂ )

- 2a ₂ airn + t ₂ ^(t l ^:

If one or both amplitude variations ai and a ₂ are known, as is sometimes the case for musical instruments whose time envelope is known in advance, their values can be substituted in the previous formula. The estimation then proceeds advantageously as according to the first embodiment.

If one or both of the amplitude variations ai and a ₂ are unknown, they can be estimated as follows. If only the amplitude variation ai is unknown, its value is estimated by canceling the derivative of-DA _n (t, t ₂ ) with respect to the amplitude variation ai:

ai = [r _n (tι) - a ₂ r _n (tι + t ₂ ) - a ₂ r _{n + tl} (t -tι) a ^a 22 ^rr nn ++ tt ₂₂ ^((tt ll ^))]] / ^{[ r} n + tι ^{(0) +} a ₂ rn + t ₁ + t ⁽ ° 2a ₂ r _{n + tl} (t ₂ )]

If only the amplitude variation a ₂ is unknown, its value is estimated in a similar way by canceling the derivative of DA _n (tι, t ₂ ) with respect to a: a ₂ [r _n (t ₂ ) - aχr _n (tι + t ₂ : air _n + tι ^(fc 2-tl ⁾ a ^a ïl ^rr nn ++ ttιι <( ^fcfc 22 ⁾ ) ^] ] [ ^r n + t ₂ ^{(0) + a} ï ^r n + t + t ₂ ( ⁰⁾ 2aιr _{n + 2} (ti)]

If the amplitude variations ai and a2 are both unknown, they are estimated according to the following iterative method. At an additional step in step E2, the circuit 2 estimates the parameters a, a ₂ , and T ₂ . First, according to the first embodiment, the circuit 2 fixes a = a ₂ = 1 and estimates the periods Ti and T2 thus without variation in amplitude. Then a ₂ = 1 is kept and the amplitude variation ai is estimated according to the previous corresponding relation for the periods t = Ti and t ₂ = 2 estimated. Then the amplitude variation a2 is estimated according to the last previous relationship for the estimated value of ai. We can repeat the previous steps by estimating Ti and T2 again, this time with the following equation:

DA _n (tι, t ₂ ) = r _n (0) + (αiti) r _{n + t} (0) +

2 2 2

(α ₂ t ₂ ) r _{n + t2} (0) + (αiti) (α ₂ t ₂ ) r _{n + tl + 2} (°)

2 (αιtι) r _n (tι) - 2α ₂ t ₂ r _n (t ₂ ) + 2αιtια ₂ t ₂ r _n (tι + t ₂ ) +

2 2αιtια ₂ t ₂ r _{n +} t ₁ (t ₂ -tι) - 2 (αιtι) 2T ₂ r _n + t _η (t∑)

2 2 (2α2t2) αιtιr _{n + 1} - ₂ (ti),

where ai = aι / Tι and α2 = 2 / T2 are slopes of the amplitude functions.

Convergence is guaranteed since each step reduces the difference DA _n D _n (tι, t ₂ ) which is internally limited by 0. Circuit 2 provides an estimate of the two periods and also of the slopes of the two amplitude functions. This information is very useful in a voice separation system based on harmonic cancellation, because it allows design a comb filter that completely removes one of the voices, even if that voice varies in amplitude.

According to a more general variant of the second embodiment, the incoming signal x is assumed to result from the sum of P periodic sounds relating to periods Ti, ... Tp, ... Tp and of amplitudes ai, ... ap,. .. ap slowly varying. If the signal x corresponds to its model, the difference function of order P:

j = n + W- \

^DA n (i, ... t _p , ... tp) Σ (XAp (XA _P _ Xp (... X ₃ ι = n

(X ₂ (Xl (i)) ... ⁾ ),

with:

XA _p (XAp_ι (i)) = XA _p _ι (XAp_2 (i)) - a _p XA _p _ι (XA _p _ ₂ (i + t _p )),

which must be zero for tp = T _p for p = 1, ... P.

The processing circuit 2 then estimates the periods Ti, ... Tp by looking for the minimum of DA _n (tι, ... tp) in the space with P variables (ti, ... tp).

The fundamental periods Ti to Tp are first estimated by supposing that the amplitudes do not vary, ie ai = ... ap = 1. Then each variation of amplitude ap is estimated by canceling the derivative of said weighted linear combination DA _n (tι, ... tp) with respect to the amplitude variation ap and evaluation of this amplitude variation for values of the autocorrelation function corresponding to the periods estimated and weighted by the amplitude variations a,. .. ap_ι already estimated, the other ap + i, ... ap being kept constant at 1. Finally the fundamental periods are estimated by evaluation of the weighted linear combination DA _n with the estimated amplitude variations, the display 4 produces the estimated periods Ti • to Tp and the slopes of the amplitude variations ai to ap or their slopes ai = iTi to αp = apTp.

Although the invention has been described for producing fundamental periods of a digital signal, the fundamental frequencies thereof will obviously be deduced by the inverse of the periods.

Claims

1 - Method for estimating several fundamental periods of a digital signal in a signal processing means (2), according to which the autocorrelation function (r _n (t)) for at least one sample (x (n)) of the digital signal is previously evaluated for predetermined variables of the periods (ti, t ₂ ) included in predetermined variation intervals (Tι _m i _n , ^τ _l max ' ^τ 2mi ^τ 2maχ) of the fundamental periods, characterized in that it comprises a determination (E2) of a linear combination (D _n ) of values of the autocorrelation function evaluated for zero at respective period variables (t , t ₂ ) and sums and partial differences thereof, and a research

(E2) of a combination of minimum value among the combinations determined in order to produce

(E3) the respective period variables for this minimum value combination as estimated periods (T, T ₂ ) •

2 - Method according to claim 1, according to which the linear combination for P fundamental periods to be estimated is a function of the type:

--n+W-1

D _n (tι, ...t _p , ...tp) Σ (Xp(Xp_ _l (...Xp(...X ₃ ι=n

(X ₂ (X _l (i))) ...) ...)

with X _p (Xp_ι(i)) = X _p -ι ₍ _{X p} _- ₂ ( _i ) ) - Xι(i) is expressed by said values of the autocorrelation function evaluated for zero, of the variables respective periods (ti, t ₂ ) and the sums and partial differences thereof.

3 - Method according to claim 1 or 2, according to which the prior evaluation of predetermined terms of the autocorrelation function r _n (t) for the sample n and the variable t is followed by a prior evaluation of predetermined terms of the following difference function: d _n (t) = r _n (0) + r _n+t (0) - 2r _n (t) in order to evaluate said linear combination (D _n ) as a function in particular of values of the difference function.

4 - Method according to any one of claims 1 to 3, according to which the linear combination is as follows for predetermined variables t and t ₂ of two periods to be estimated:

D _n (tι,t ₂ ) = d _n (tι) + d _n+t2 (tι) - 2r _n (t ₂ ) + 2r _n (tι+t ₂ ) + 2r _n+tl (t ₂ -tι) - 2r _n +t ₁ (2)

5 _ Method according to claim 1 characterized in that, when the digital signal is supposed to result from component signals having respectively said fundamental periods (T, T ₂ ) and amplitude variations (a, a ₂ ) during said periods, the values of the autocorrelation function evaluated for respective period variables (t, t ₂ ) and partial sums and differences thereof in the linear combination are weighted respectively by one of the amplitude variations, squares of these and the products of these, after estimation of the amplitude variations. 6 - Method according to claim 5, according to which the fundamental periods are first estimated assuming that the amplitudes do not vary, then each amplitude variation (ap) is estimated by canceling the derivative of said weighted linear combination ( DAp) with respect to the amplitude variation and evaluation of said amplitude variation for values of the autocorrelation function corresponding to the estimated periods and weighted by the amplitude variations already estimated, and finally by another estimation of the periods fundamental by evaluating the weighted linear combination (DA _n ) with the estimated amplitude variations.

7 - Method according to claim 5 or 6, according to which the linear combination for P fundamental periods to be estimated is a function of the type:

i=n+W-l

DA _n ₍ tι, ...t _p , _... tp) = ∑ (XAp(XA _P _{_ι} (... ...)) ² ,

with: XA _p (XAp_ι(i)) = XAp-i(XAp- ₂ (i) ) - a _p (XA _p - ₂ (i+t _p )

for 1 < p ≤ P, in which the function XAι(i) is expressed by said values of the autocorrelation function evaluated for zero, of the respective period variables (ti, t2) and the sums and partial differences thereof .

8 - Method according to any one of claims 5 to 7, according to which the linear combination is as follows for variables predetermined i and T2 and amplitude variations ai and a ₂ relating to two periods to be estimated:

DA _n (tι,t ₂ )=r _n (0) + ïr _n+tl (0) + _a J5r _n+t2 (0) + aιa _{2 n+tl + t2} (0) - 2aιr _n (tι) - 2a ₂ r _n (t ₂ ) +

2aιa ₂ r _n (tι+t ₂ ) + 2aιa ₂ r _{n+ tχ} (t ₂ -tι) - 2 _a fa ₂ r _{n+ tl} (t ₂ )

9 - Method according to any one of claims 1 to 8, according to which the search consists of searching for a first minimum value among combinations determined for the variation interval relating to a first period and predetermined constant values of the other periods, then a second minimum value among combinations determined for the first minimum value and the variation interval relating to a second period and predetermined constant values of the other periods, and so on until obtaining a minimum value of the lower linear combination at a predetermined threshold.

10 - Method according to any one of claims 1 to 9, according to which the autocorrelation function is smoothed.