## 4 IMel Spectrogram
### Generation of the IMel Spectrogram  
The IMel spectrogram is generated by using an improved IMel filter bank, and the transformation relation is as follows:  
\[f_{IMel}=2595\times\exp(1+f_{lin}/700) \tag{2}\]  
\(f_{IMel}\) is expressed in the IMel frequency domain, which is opposite to the Mel frequency domain. Figure 4a shows the exponential relationship between \(f_{lin}\) and \(f_{IMel}\) in the IMel frequency domain. As shown in Figure 4b, the high-frequency part of the IMel filter banks has a narrow bandwidth and high resolution, thus enhancing the influence of high-frequency signals. Therefore, the IMel spectrograms generated using the IMel filter banks have the same characteristics. Figure 4: (**a**) The relationship between \(f_{lin}\) and \(f_{IMel}\). (**b**) The IMel filter banks. Figure 3: [PERSON]’s two-dimensional emotion spatial representation. Figure 5a,b show the same person saying the same sentence \"The dog is sitting by the door\" with different emotions. In Figure 5a, anger is intense and quasi-periodic, with higher energy and more low-frequency parts. The speech in Figure 5a has the Mel spectrogram shown in Figure 5c, with clear stripes, highlighting the emotional information of the high-arousal signal. In Figure 5b, the speech is sad, weak, and low in energy, the range of the ordinate is [\(-\)0.1,0.1], which is ten times smaller than the range of angry speech. The unvoiced segment \"S\" in Figure 5b, marked by the ellipse, is the key point of detection. The Mel spectrogram in Figure 5d and the IMel spectrogram in Figure 5f corresponding to \"S\" are displayed in the ellipses. The IMel spectrogram amplifies the role of the high-frequency part and highlights the emotional information of the low-arousal signal. This paper combines the Mel spectrogram highlighting the low-frequency part with the IMel spectrogram highlighting the high-frequency part to apply their complementary effects to SER. As shown in Figure 6, the speech signal is preprocessed, and then the energy obtained after a fast Fourier transform (FFT) is calculated. After passing through the Mel filter banks and the IMel filter banks separately, the logarithm is calculated, and finally the Mel spectrogram and the IMel spectrogram are obtained. The steps performed to generate the IMel spectrogram are as follows:  
Figure 5: (**a**) Speech signal of anger. (**b**) Speech signal of sad. (**c**) Mel spectrogram of anger. (**d**) Mel.spectrogram of sad. (**e**) IMel spectrogram of anger. (**f**) IMel spectrogram of sad. Figure 6: The generation of Mel spectrogram and IMel spectrogram. 1. The speech signal \(x_{s}(n)=[s_{1}(n),s_{2}(n),\cdots,s_{i}(n),\cdots,s_{l}(n)]\) is framed, where \(s_{i}\) represents each frame and \(l\) denotes the number of frames. 2. Windows \(s^{\prime}_{i}(n)=s_{i}(n)\times w(n)\) are added, where the window function \(\omega(n)\) is a Hamming window and \(n\) is the window length. 3. Each frame of the signal \(s^{\prime}_{i}(n)\) is transformed by FFT, \(X_{i}(r)=\sum\limits_{n=0}^{N-1}s^{\prime}_{i}(n)\times e^{-2\pi r/N}\), \(r=0,1,\cdots N-1\) and the energy \(S_{i}(r)=\left|X_{i}(r)\right|^{2}\) is obtained. is the number of points of the FFT. 4. \(f_{l}\) and \(f_{h}\) are converted from a linear scale to the IMel scale and are expressed as \(f_{l}\)' and \(f_{h}\)': \[f^{\prime}_{l} =2595\times\exp(1+f_{l}/700)\] (3) \[f^{\prime}_{h} =2595\times\exp(1+f_{h}/700)\] (4) where \(f_{l}\) and \(f_{h}\) are the lowest frequency and the highest frequency of the filter frequency respectively. 5. The center frequency of each filter in the filter banks is Calculated: \[f^{\prime}_{c_{j}}=f^{\prime}_{l}+j\times(f^{\prime}_{u}-f^{\prime}_{l})/(M+1)\] (5) where \(j=1,2,\cdots,M-1\), \(M\) is the number of filters. 6.