# Harris Hawks Sparse Auto-Encoder Networks for Automatic Speech Recognition System
## 3 Methodology
### Harris Hawks Sparse Auto-Encoder Networks (HHSAE)-ASR Framework
#### 3.2.1 Speech Signal Preprocessing and Denoising  
Here, the spectral deduction approach is applied to the collected speech signal to purify the signal. The method effectively apprises the spectrums in the most straightforward and easiest ways. The spectrum is not affected by time due to the additive noise. For every speech signal \(s(n)\), it has a clean signal \(cs(n)\) and an additive noise signal \(ad(n)\). Therefore, the original speech signal is written as Equation (1).  
\[s(n)=cs(n)+ad(n) \tag{1}\]  
The clean signal \(cs(n)\) is obtained by applying the discrete Fourier transform with the imaginary and the real part, which gives the noise-free speech output signal. The Fourier transform representation of the signal is defined in Equation (2).  
\[s(w)=cs(w)+ad(w) \tag{2}\]  
Figure 1: Outline of HHASE-ASR framework that includes speech input, speech preprocessing, feature extraction, speech recognition, and speech-to-text modules.  
\[s(w)=s|(w)|e^{i\mathcal{O}s} \tag{3}\]  
The Fourier transform of signal \(s(n)\) is obtained by computing the spectrum magnitude \(s|(w)|\) and the \(\varnothing\) phase spectra value of the noise signal is obtained using Equation (4).  
\[ad(w)=|ad[w]|e^{i\varnothing\overline{\mathcal{O}}} \tag{4}\]  
The value of the computed noise spectrum value \(|ad[w]|\) is more helpful to identify the noisy information of the original speech signal. This noise continuously occurs in a loud and noisy environment, which completely affects the originality of the speech. Therefore, the noise value in \(s(w)\) should be replaced by the average noisy spectrum value. This average value is computed from the details of nonspeech activities (speech pause) and speech ineligibility (s) because it does not affect the speech quality. Therefore, the noise-free signal is computed as:  
\[cs_{e}[w]=[|s(w)|-|ad_{e}[w]|]e^{i\varnothing\overline{\mathcal{O}}} \tag{5}\]  
The clean signal \(cs_{e}[w]\) is estimated from the computation of the signal spectrum magnitude \(s|(w)|\) of the phase spectrum value and the average noise spectrum value of the noise signal \(|ad_{e}[w]|\). The spectral magnitude is computed to clean the recorded speech signal.  
Extraction of features is used to train a [PERSON] model-based convolution network for resolving noisy and loud voice signals. According to the hawk's prey finding behavior, the network's parameters are fine-tuned and updated during this process. The system's robustness and availability are maintained by reducing the number of misclassification errors.  
\[cs_{e}[w]=[|s(w)|-|ad_{e}[w]|] \tag{6}\]  
Then, Equation (6) is applied to identify the power spectrum of the speech signal \(s(w);cs_{e}[w]^{2}=|s(w)|^{2}-|ad_{e}[w]|^{2}\) to estimate the original noise-free signal. The computed spectral values cut off the noise information from the original signal \(s(n)\). Then, the inverse Fourier transform is applied on the signal magnitude \(|cs_{e}[w]|\) and the power spectrum \(\left|cs_{e}[w]^{2}\right|\) to identify the noise-free speech signal.  
\[cs_{e}[\omega]p=|s(\omega)|p-|ad_{e}[\omega]|p \tag{7}\]  
The noise-free signal is computed from the spectral subtraction of the power exponent \(p\). Here, the noise signal spectrum deduction is performed according to \(p\). If the \(p\) has a value of 1, then magnitude is affected by noise and that part is deducted from the signal. If the value of \(p\) is 2, the power spectral deduction is applied to obtain the original noise-free signal. Then, the noise removal of the speech signal is summarized in Figure 2.