# Tests of the Influence of DAF (Delayed Auditory Feedback) on Changes in Speech Signal Parameters
## 4 Result and Discussion
Monitoring fundamental frequency is essential for accurate sound production and speech intelligibility. It also reflects emotional changes such as stress, tension, or uncertainty. Figure 3: Approximate speech tempo results for women at the given delays for each of footography (fot). Formants are acoustic resonances generated during speech production, representing frequency bands with increased energy in the sound spectrum. These resonances are shaped by the articulatory system, including the throat, oral cavity, and nasal cavity. Special attention is given to the first and second formants: the first is related to the oral cavity, while the second reflects the tongue position. Other formants are associated with individual voice characteristics, such as timbre. Naturally, women exhibit higher formant values compared to men. Figure 4: Approximate speech tempo results for men at the given delays for each of footgraphy (fot). The process of formant estimation in Praat is based on spectral analysis of the speech signal and the identification of resonant frequencies corresponding to local maxima in the amplitude spectrum. A crucial part of this analysis involves both autocorrelation and Fourier transformation techniques, applied within moving time windows. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{**Las**} \\ \cline{2-10}  & **Delay** & **Laryngeal Tone** & \multicolumn{4}{c}{**Formants**} & **Jitter** & **Shimmer** & **Time** \\  & **[ms]** & **[Hz]** & **1** & **2** & **3** & **4** & **[\%]** & **[\%]** & **[\%]** \\ \hline \multirow{4}{*}{w1} & 0 & 231.88 & 827.60  
Initially, the speech signal is divided into short time frames. Each frame is then multiplied by a window function, \(\omega(t)\), using Hamming window, which helps minimize edge effects and improves frequency resolution. \[a(t)=\left(x\left(t_{mid}-\frac{T}{2}+t\right)-\mu_{x}\right)*\omega(t) \tag{1}\]  
\(t_{mid}\)--center of the analyzed frame;  
\(T\)--window length;  
\(t\in[0,T]\)--sliding variable within a window;  
\(\mu_{x}\)--average signal value in the analyzed fragment. Next, the normalized autocorrelation \(r_{a}(\tau)\) function is computed, allowing for the identification of dominant periodicities in the signal. The peak values of this function correspond to the dominant resonant frequencies. \[r_{a}(\tau)=r_{a}(-\tau)=\frac{\int_{0}^{T-\tau}a(t)a(t+\tau)dt}{\int_{0}^{T}a ^{2}(t)dt} \tag{2}\]  
The implementation requires performing a Fourier transform followed by increasing the resolution of the frequency domain. \[\widetilde{a}(\omega)=\int a(t)e^{-i\omega t}dt \tag{3}\]  
The next step is to compute the inverse Fourier transform of the power spectral density, which enables a transition to the delay domain. \[r_{a}(\tau)=\int\left|\widetilde{a}(\omega)\right|^{2}e^{i\omega\tau}\frac{d \omega}{2\pi} \tag{4}\]  
In the article by [PERSON], the creator of Praat, two methods of pitch analysis are described--zero-phased and cepstral--along with a discussion of their differences [30]. However, the current version of Praat employs an algorithm based on the Linear Predictive Coding (LPC) model. This method relies on the autocorrelation of the speech signal and models it as a resonant system, thereby indirectly utilizing spectral information. Regarding formant stability, the men demonstrate greater susceptibility to changes under DAF conditions, particularly for the vowels 'I' and 'U'. In contrast, women display more stable voice modulation under the same conditions, as shown in the graphs below (Figures 5 and 6). It is important to note that the obtained results are fully reliable, as no artificial conditions were imposed, requiring the participants to sustain vowels in isolation for several seconds. Instead, the analysis focused on vowel segments extracted from spontaneous speech recorded during the description of photographs. This data collection approach preserves naturalness and enhances the validity of the results within the context of the study's conditions.