## 3 Modification of MCRA Algorithm
### Variable Segment Length Adapted by Harmonic Properties  
Harmonic properties are utilized to determine the segment length \(L\) that controls the period for the update of noise estimate. Initially, the number of harmonic spectra is utilized to determine whether a frame is a vowel. If the frame is detected as a vowel, the segment length \(L\) increases. This increases the period for the search of spectral minimum as given in (14), yielding noise spectrum being underestimated. Conversely, the segment length \(L\) decreases when a noise-dominant frame is detected. The segment length is expressed by  
\[L(l)=\left\{\begin{array}{l}L(l)+L_{1}\;,\text{if}\;F^{\text{\tiny{0}}}(\eta )=1\\ L(l)+L_{2}\;,\text{if}\;\sum\limits_{t=-\varepsilon}^{\varepsilon}F^{\text{ \tiny{0}}}(\eta+t)>0\\ \beta*L(l)\quad,\text{otherwise}\end{array}\right. \tag{15}\]  
where \(l\) is the segment index. \(L_{1}\) and \(L_{2}\) represent the length increment of segment for updating \(P_{tmp}(\eta,\Omega)\) given in (13) in a vowel and the corresponding neighbor regions, respectively. They are empirically chosen to be 63 and 12, respectively. \(\varepsilon\) controls the neighbor frames to be included for the regions of onset, offset, and consonants. It is set to be 3. \(\beta\) controls the decrement ratio of segment length for noise regions. It is empirically chosen to be 0.9. \(F^{\text{\tiny{0}}}(m)\) is a vowel flag, expressed by  
\[F^{\text{\tiny{0}}}(\eta)=\left\{\begin{array}{l}1\;,\text{if}\;\eta^{th} \;\text{frame}\;\in\;\text{vowel}\\ 0\;,\text{otherwise}\end{array}\right. \tag{16}\]  
In (15), the segment length significantly increases with \(L_{1}\) frames when a frame is detected as a vowel. Conversely, the segment length decreases with a ratio of 0.9 of the current segment length, i.e., 0.9-L, when a frame has been detected as speech absence. A consonant may appear in the precedence of a vowel for spoken Mandarin Chinese. We increased the segment length slightly with \(L_{2}\) frames, yielding noise magnitude being underestimated. This enables a consonant to be preserved by the process of speech denoising. In the regions of onset and offset during a vowel, the segment length also increases slightly with length \(L_{2}\).  
Figure 1 shows the contour of detected minimum power, which is employed to determine the value of the speech indicator given in (7) and (8). The smaller the detected minimum of the magnitude is, the higher the speech presence probability is. In the case of speech-pause regions, the proposed method can improve the MCRA method by well tracking the variation of interference noise, in particular during frames 0 to 40 and frames 380 to 400. So the level of interference noise can be estimated well. This is attributed to the segment length, which has been shortened by the factor \(\beta\) (0.9) as given in (15). The estimate of minimum power updates quickly. Accordingly, the quantity of background noise in denoised speech effectively reduces, yielding denoised speech sounding less annoying than that using the MCRA noise estimator. Conversely, the MCRA method is unable to track the variation of noise spectrum very well. Plenty of residual noise exists in denoised speech. In the case of weak vowels, the segment length increases during a vowel as well as its neighbor frames (during frames 255 to 300). This enables the minimum power to be underestimated. The corresponding value of speech presence probability increases, yielding the quantity of speech components with weak energy, such as weak vowels and consonants, which is then preserved when speech denoising is performed. The speech distortion in the denoised signal is reduced.