PAR is a difficult problem, mainly due to the specific material to interpret: the voice signal. The speech acoustic signal has characteristics that make complex interpretation.

Redundancy: the acoustic signal carries much more information than necessary, which explains its resistance to noise. Of analytical techniques were implemented to extract relevant information without too degrading it.

Variability: the acoustic signal is highly variable from one speaker to the other (gender, age, etc.) but also for a given speaker (emotional state, fatigue, etc.), which makes very difficult the recognition problem speaker’s independent speech.

Continuity: the acoustic signal is continuous and contextual effects of sound on elementary visions are considerable.

By speech processing we mean the processing of the information contained in the speech signal. The objective is the transmission or recording of this signal, or its synthesis or recognition. The speech processing is now a fundamental component of the engineering sciences. Located at the intersection of digital signal processing and language processing (that is to say, symbolic data processing), this scientific discipline has known since the 60s a rapid expansion, linked to the development of means and telecommunications techniques. The special importance of speech processing in this broader context is explained by the privileged position of the word as an information vector in our human society.

The ACOUSTIC MODEL (Figure 1) reflects the acoustic realization of each modeled element (phoneme, silence, noise, etc.). It is based on the concept of phonemes. Phonemes can be considered as the basic sound units in verbal language. The first stage of speech recognition is to recognize a set of phonemes in words flow. Statistical realization of acoustic parameters of each phone is represented by a Markov model Cache (HMM: Hidden Markov Model). Each phoneme is typically represented by 2 or 3 states and density multigaussienne (GMM: Gaussian Mixture Model) is associated with each state. See Figure 2 below.

The speech signal (picked up using a microphone) is first digitized: it is sampled by a Fourier transformation which calculates the energy levels of the signal in bands of 25 milliseconds, which strips overlap in 10 milliseconds time.

The result is compared with prototypes stored in computer memory in both a standard dictionary and a speaker’s own dictionary. This dictionary is constructed by initially sessions dictation standard texts that the speaker must make before effectively use the software. This own dictionary is regularly enriched by self learning during the software uses. It is interesting to note that thus constituted voiceprint is relatively stable for a given speaker and little influenced by external factors such as stress, colds, etc. (Figure 3).

It is generally divided into two part linked to language: a syntactic part and a semantic game. When ACOUSTIC MODEL has identified at best phonemes “heard”, we still look the most likely message M corresponding thereto, that is to say, the probability P(M) defined above. It is the role of syntactic and semantic models. See Figure 4 below.

From the set of phonemes from the ACOUSTIC MODEL The SYNTACTIC MODEL will assemble phonemes into words. This work is also based on a dictionary and gram-

mar standards (The language “Baoule” has one) as well as a dictionary and a grammar own speaker; these reflect the “habits” of the speaker and is continuously enriched. Then SEMANTIC MODEL seeks to optimize the identification of the message by analyzing the context of the words and while basing on both its own common language semantics and on cleanning the speaker semantics (a style). This modeling is usually built from the analysis of sequences of words from a large textual corpus. This clean semantics will be enriched as you use the software. Most softwares also allow enriching the analysis of texts that reflect the stylistic habits of the speaker. These two modules work together and it is easy to conceive that there is a feedback between them.

Initially, the dictionary associated with these two modules were based on fixed syntax language models, that is to say, modeled on a grammar defined by a rigid set of rules (this is not the case in most African languages including the “Baoule” language).

Then, the voice recognition software has evolved into the use of local probabilistic models: recognition no longer performs at a word but at a series of words, called n-gram where n is the length words in a sequence .The statistics of these models are obtained from standard texts and may be enriched gradually. See Figure 5 below.

Here too, Hidden Markov Models are those currently used to describe the probabilistic aspects. the most advanced software tend to combine the advantages of statistical models and fixed syntax models in what is called the “probabilistic grammars”, the idea being to derive from fixed grammars of probabilities that can be combined with those of a probabilistic model. In recent approaches, it becomes difficult to distinguish the syntactic model of the semantic model and we rather speak of a single language model.

We first present a first method (basic but inefficient) to calculate the probability dis- tribution of observations.

Proposal: The probability distribution of observations is given (in the digital case) by

for any sequence.

Note that elementary method provides a first expression for the conditional probabi- lity distribution of the sequence of states given observations (in digital case):

and the likelihood of the model (obtained using the following observations in place of dummy variables):

we deduce the following identities:

.

Note the number of operations required to calculate the probability distribution of observations from this basic method is significant for each possible path of the Markov chain, you must compute the product of words, and there is different possible paths the total number of elementary operations (additions and multiplications) thus made is of the order of the number is growing exponentially with the number n of observations. we define the forward (seen as a row vector) by for all.

Note the forward variable used to calculate the conditional probability distribution of

the present state given observations:

for all. (In this sense, is a distribution of non-normalized probability), and the normalization constant is interpreted as the likelihood of the model given observations.

Theorem: The sequence satisfies the following recurrence equation:

for all with the initial condition for any.

Note this statement result component-by-component can also be made for the variable forward view as a row vector and.

Note the recursive calculation of the variable forward involves only the product matrix/vector, and to calculate more efficiently the probability distribution of obser- vations simply elementary operations (additions and multi- plications) to move from time k to time the total number of elementary operations to be performed is thus of the order of: this number grows only linearly with the number n of observations.

Digital implementation: Instead of first solving the equation for the forward non-standardized version of the conditional distribution, defined at any time k as for all and then deduct the normalization constant (likelihood) and the normalized version of the conditional distribution (filter)

and

It is more efficient, on a digital point of view, spread directly log-likelihood and filter.

Proposal: Following Verie the following recurrent equation:

for all with the initial condition

for any.

where the normalization constants are defined by and.

Note this result statement component-by-component may also be formulated for the

normalized forward variable seen as a row vector and

where the normalization constants are defined by and.

Note: Following truth the following recurrent equation:

with the initial condition and iterating log. For all intermediate time k, less than the final instant n, is defined for all.

Note: That variable allows to calculate the conditional probability distribution of the

present state knowing all comments,

for all with the normalization constant.

Note: Fix the state at time k allows a break between the past up to time and the future from time. This justifies the introduction of the variable backward (seen as a column vector) and defined as:

for any

and in particular for all with this definition, is obtained for all.

Note: Conditionally the X_ suite to come hidden states is a Markov chain, from initial law (line i the matrix), that is to say that for all and transition matrix it follows that the backward variable can be interpreted as the likelihood of the model derived from the state at time k given observations.

Theorem:

After Verie recurrent retrograde following equation:

for all with the initial condition: for all.

Note: This result statement component-by-component can also be formulated for the backward view variable as a column vector and.

Proposal: the forward and backward equations are dual to one another:

not dependent of the time in question

Proposal: For the distribution of conditional probability of transition at an intermediate time given observations until the final moment is given by:

for all

By summing for all and using the equation backward, or by summing for all i ∈ E and using the forward equation, we find the following results in terms of product component-by-component variables forward and backward.

Corollary: the conditional probability distribution of the present state knowing

all comments is given by with the definition

for all.

Note: Verie one that constant Standards

and

do not depend on the time in question, and are interpreted as the likelihood of the model given observations. instead of first solve the backward and forward equation equation separately, and to successively deduct the non-normalized version of the conditional distribution, defined at any instant k as for all

then the normalized version of the conditional distribution (smoother)

.

It is more efficient on a digital point of view, spread directly log-likelihood and filter,

then spread the variable defned at any time k as for any.

Note: That with normalization of the backward variable, the conditional probability distribution of state given observations is expressed as

for all.

Proposal: Following Verie recurrent retrograde following equation:

for all, with the initial condition: for all

where the normalization constants are those already defined for the normali- zation of the variable forward.

Note: This result statement component-by-component can also be formulated for

backward standardized variable viewed as a column vector and

where the normalization constants are those already defined for the normalization of the variable forward.

Note: It is noted that for all

And postponing this identity in the expressions obtained above, we Verie that the conditional probability distribution of the transition given observations is expressed as

for.

Forward and backward variables used to calculate the conditional probability distribution of the state this, or state at an intermediate moment, given observations

defined by for all, and

for any respectively, where the normalization con-

stant does not depend on the time in question, and interprets as the likelihood of the model given observations. it is not necessary to calculate the conditional average, but can be used however the estimator of maximum a posteriori, which minimizes the likelihood of the estimation error given observations and defined for the present state

and for the state to an inter-

mediate time by it may hap-

pen that the sequence generated is inconsistent with the model, in the following sense: it can happen that is obtained and for two successive times, while for the same pair, which meant that the transition from state i to state j is just impossible for the model for this reason, rather it uses another estimator, called trajectoriel maximum a posteriori estimator, defined by.

And minimizes the probability of the estimation error of the sequence of hidden states given observations it is of course not possible to perform this maximization exhaustive manner, listing all possible trajectories: the efficient calculation of this estimator is provided by a dynamic programming algorithm called Viterbi algorithm.

So far, the focus was on the estimation of a hidden condition or because of successive hidden states, from a series of observations and for a given model. The goal here is to identifier the model, that is to say, to estimate the parameters of the model characteristics, from a series of observations, and the approach taken is that of estimation maximum likelihood.

In the digital case, we look at the case of the Gaussian emission densities characterized by the data of finite vectors and of finite Family matrices invertible covariance, that is to say:

The likelihood function of the model admits expression

obtained with the basic method, and we will study an iterative algorithm to maximize likelihood function with respect to the parameters model of either another model, for which the likelihood function takes the value

the (log) likelihood ratio between the and the is reduced by

which vanishes when the model coincides with the model.

Maximize compared with parameters of the model thus ensures that the likelihood of the model which achieved maximum will be greater than the likelihood current model re-formulas Baum-Welch -Estimated allow explicitly find the parameters of the new model based on parameters of the current model by repeating this procedure, we construct a sequence of increasing likelihood models, and ideally this sequence converges to a model that reaches the maximum likelihood function.

Theorem

In the digital case with densities of Gaussian issue, the iterative algorithm for esti- mating the maximum likelihood of the model parameters from the observations, is given by explicit formulas re-estimate

and and

and

for all where the two sequences and are the standard equations of forward and backward solutions respectively for values parameters.

Note: Concretely, if denotes the current model in step of the algorithm, then for values the para- meters are calculated standardized solutions and of equations forward and backward respectively the parameters is calculated using the formulas to re-estimate what defines the new model to s next step of the algorithm.

During the learning phase, it is necessary to record the repeated statements of each digit in the dictionary. For example, we repeat the word “nnou” (which means five in “Baoule” language) many times with a pause between each statement. That word will be saved in the file 'cinq.wav'. Using the following MATLAB code with a sound card standard PC, we capture ten seconds of speech from a microphone to 8000 samples per second. We obtained y that is a matrix of 8000 rows and one column. This approach works well for training data.

We first develop a word-detection algorithm that separates each word of ambient noise. We then obtain an acoustic model that provides a strong representation of each word in the stage of learning. Finally, we select an appropriate classification algorithm for testing.