Mathematical model of speech signal leakage channels during discrete-quantified conversion
The purpose of the article is to estimate the leakage channel of a discrete-quantized speech signal with amplitude-pulse modulation. Discrete-quantized analog-to-digital conversion of signals in the article is considered by the example of pulse-amplitude modulation. Development of mathematical model of speech signal leakage channels during discrete-quantified conversion is based on the spectral representation of periodic signals by Fourier series. A periodic pulse train of triangular shape as a measuring signal is proposed. Measuring signal of triangular shape has an advantage over a harmonic signal in the process of quantization noise extraction because it allows one to achieve higher accuracy during signal processing. To evaluate the channel security caused by amplitude-pulse modulation, a harmonic signal is used, which is generated from a periodic pulse sequence of a triangular shape by the Fourier transform method. As a result of constructing the spectrum of the amplitude-pulse modulated signal, it was found that for each harmonic component of the spectrum corresponding to the spectrum of the periodic sequence of pulses, side components corresponding to the spectrum of the modulating signal appear. This side components, together with the low-frequency component in the band of the speech signal, form an information leakage channel. The presence of source modulating signal in the amplitude-pulse modulated signal spectrum allows one to digest the security of the leakage channel of the speech signal with amplitude-pulse modulation by the low-frequency component of the modulating signal. The materials presented in the article are original and can be used in assessing the security of leakage channels of speech signals converted into digital form. In addition, the results obtained allow further studies of the security of speech signals during their inverse transformation from digital to the original signal.