A new blind separation method for under-determined speech signals based on single source interval pre-extraction

A new method is proposed to realize the blind separation of speech signals under underdetermined conditions. Before estimating the mixed parameters, the single-source interval pre-extraction operation first "filters" out a part which is obviously not a single source. The time-frequency interval of the source analysis domain category.The simulation results show the good performance of the algorithm.


Introduction
How to identify the sound source of interest from a noisy environment and obtain a clear voice is an urgent problem to be solved. For a speech signal, the strength of the signal and the change of intonation determine its non-stationarity, and the speech signal involved in this article is a typical non-stationary signal. Different times, occasions, and people will change this non-stationary law and make it more difficult to solve the problem.

Blind source separation of speech signal
In the speech processing system, blind source separation is mostly used for speech recognition, that is, to separate and reconstruct the original speech signal from a large number of mixed speech signals [1] .
The block diagram of the system model is shown in Figure 1.
In the figure, , , N s t s t s t are the N unknown source signal, x t are the M observation signal output by the receiving array element, and satisfies N M > . The source signal and mixed signal are expressed in vector form, as follows [2][3] : The mixing process can generally be seen as a mapping from

Single source interval pre-extraction
Through research of TIFROM algorithm and TIFCORR algorithm based on the two single-source interval detection algorithms [4] , it can be found that when it is used to deal with the under-determined blind source separation model, as the number of source signals increases, the two algorithms are Errors will occur in the search of intervals, and it is not guaranteed that the search results of a single source interval are optimal each time, resulting in poor algorithm performance [5][6] . In order to effectively identify the single-source interval, this paper introduces the single-source interval pre-extraction algorithm. Before estimating the mixed parameters, the single-source interval pre-extraction operation is used to "filter" a part of the time-frequency that obviously does not belong to the single-source analysis domain. Interval.
In practical applications, the process τ ω τ ω τ τ τ ω ∀ ∈ of discriminating any two points in the interval that satisfies equation (8) requires a large amount of calculation. Therefore, this paper takes the absolute value of the maximum difference in the interval, then the time-frequency interval that satisfies the formula (9) must satisfy the formula (8).
Equation (9) is the single-source interval extraction criterion, and any time-frequency interval in the real-time frequency domain that satisfies equation (9) will be extracted as a single-source interval (the value of P is generally 3 5 ).

Simulation verification
Next, take the under-determined hybrid system with four source signals and two receiving sensors as an example, and verify the article by comparing the time-frequency ratio and phase difference histograms of the two observation signals before and after the single source interval pre-extraction. The validity of the single-source interval extraction criterion.
It can be seen from Figures 2 to 5 that before the single source interval extraction, the distribution of the modulus ratio and phase difference of the sum of the two observation signals is very dense. However, after the single-source interval extraction, the statistical distribution characteristics of the modulus ratio and the phase difference are very obvious, and most of the useless data is filtered out at the same time, which reduces the computational complexity of estimating the parameters of the mixed matrix. Figures 6 and  7 are the scatter plots of the modulus ratio and phase difference before and after the single source interval extraction.

Result analysis
It can be seen from Figure 6 that the scatter plot distribution of the modulus ratio and phase difference of the original data is irregular. The data after single-source interval detection shows good aggregation, which can prove that the single-source interval pre-processing algorithm has a good preprocessing effect. The time-frequency interval that is obviously not in the single-source analysis domain is eliminated, the efficiency of speech source signal extraction is improved, and a good foundation is laid for the correct extraction of speech signal in the next step.