Within the framework of a dynamically developing direction of research in the field of acoustic measurements, the task of spectral analysis of speech signals in automatic speech recognition systems is considered. The low efficiency of the systems in unfavorable speech production conditions (noise, insufficient intelligibility of speech sounds) compared to human perception of oral speech is noted. To improve the efficiency of automatic speech recognition systems, a two-stage algorithm for spectral analysis of speech signals is proposed. The first stage of speech signal processing consists of its parametric spectral analysis using an autoregressive model of the vocal tract of a conditional speaker. The second stage of processing is the transformation (modification) of the obtained spectral estimate according to the principle of frequency-selective amplification of the amplitude of the main formants of the intra-periodic power spectrum. The software implementation of the proposed algorithm based on the high-speed computational procedure of the fast Fourier transform is described. Using the author’s software, a full-scale experiment was carried out: an additive mixture of vowel sounds of the control speaker’s speech with white Gaussian noise was studied. Based on the results of the experiment, it was concluded that the amplitude of the main speech signal formants were amplified by 10–20 dB and, accordingly, a significant improvement in the speech sounds intelligibility. The scope of possible application of the developed algorithm covers automatic speech recognition systems based on speech signal processing in the frequency domain, including the use of artificial neural networks.