# The Use of Correlation Features in the Problem of Speech Recognition
## 3 Materials and Methods  
Twenty typical phraseological exchange phrases were selected from the aviation rules in Russian for further processing and recognition of speech commands. Ten speakers were involved. Every speaker wrote down each phrase 10 times. Thus, the size of the initial sample was 2000 sound recordings. Primary data processing, which consists in the formation of time sequences, was performed in the Audacity program [56]. A typical signal from the phrases \"Pre-flight check of communication\" and \"Ready for take-off\" is shown in Figure 1. From left to right are the recordings of three different speakers. Note that the abscissa shows not the signal pressure but the modulation of voice using voltage after microphone recording. The \(X\)-axis is the time axis in seconds. Figure 1: Time series of studied radio messages. In Figure 1a, we see what time series are obtained when pronouncing the phrase \"Pre-flight check of communication\" by different speakers. Obviously, the content of the speech message itself has more weight on the generated signal than the speaker who pronounces it. Similarly, Figure 1b shows the representations of the phrase \"Ready for take-off\" by different speakers. Figure 2 shows the spectra of messages shown in Figure 1. In this case, the \(X\)-axis will represent the frequency range (f) in Hz, and the \(Y\)-axis represent signal level (S) in dB. Note that by analogy with Figures 1a and 2a shows the spectra of the speech signal \"Pre-flight check of communication\" recorded by three different speakers. Figure 2b shows the spectra of the speech message \"Ready for take-off\". It can also be noted that the influence of the content of the message on the generated spectrum is much greater than the influence of the speaker The frequency range that differs in men and women can be interesting. However, aviation is currently dominated by men as pilots. In the Audacity program, the available frequency range is from 0 to 21.9 kHz. When quantizing 8 bits, it is divided into 256 levels, on which the spectrum is analyzed. The advantage of switching to the spectral representation is that the processing becomes invariant to the signal duration, but the spectrum is highly dependent on the speaker, which can introduce recognition errors. Note that 256 spectral characteristics per record increase the amount of data to almost 600,000 examples. In this regard, it was decided to decimate the spectra based on the average value. Thus, compressed (averaged) features of the spectrum were additionally extracted for faster processing,  
Figure 3 shows the spectra of all studied phraseological radio exchange messages. Note that the graph has a logarithmic scale along the \(X\)-axis, where the frequency is reflected, and the signal level in dB is plotted on the \(Y\)-axis. For the convenience of visualization, we also averaged all records of all speakers for each phrase. Figure 2: The spectrum of the studied radio messages. The next preprocessing step is to convert the values from dB to V. The reference voltage was taken as \(U_{0}=1\) mV. Then it is possible to use the following relationship between the quantities:  
\[S[\text{dB}]=10\log(U/U_{0}), \tag{1}\]  
where \(S\) is the spectrum in [dB], \(U\) is the spectrum in [V], and \(U_{0}\) is the reference voltage. So, Formula (1) is needed to determine the desired voltage  
\[U[\text{V}]=10^{5/10-3}. \tag{2}\]  
Using expression (2) for each component of the spectrum, it is possible to obtain the amplitude spectrum of voltages. For the data in Figure 4 similar spectra were plotted. However, the \(Y\)-axis now also uses a logarithmic scale. Figure 3 shows examples for all of the studied speech commands. Since we have carried out averaging procedures, we can consider the obtained spectra as standards for each message. It should also be noted that all schedules have a similar structure, but at the same time, each message has its own peculiarities. Our next task is to get a more vivid representation of them.