# Whispered Speech Conversion Based on the Inversion of Mel Frequency Cepstral Coefficient Features
## 2 Whispered Speech Conversion Process
### Inversion of Speech Features
Phase spectrum estimation We used the least squares method to estimate the speech frame from the power spectrum, i.e., the power spectrum was square-rooted and then converted into an amplitude spectrum. An appreciable amount of phase information is lost when obtaining the power spectrum by feature extraction; thus, it is important to recover the phase spectrum. The least square method with the inverse short-time Fourier transform magnitude (LSE-ISTFTM) algorithm was used to modify the discrete Fourier transform (DFT) and inverse discrete Fourier transform (IDFT) to estimate the phase spectrum [30], which, in combination with the given amplitude spectrum, was then used to estimate the speech for each frame in the time domain. Finally, the speech was reconstructed by adding and overlapping the sequence of speech frames. The LSE-ISTFTM Algorithm 1 process is as follows:```
1:Input: Amplitude spectrum, \(\left|\widetilde{X}\right|\); Number of iterations, M
2:Output: Estimated speech frame, \(\hat{x}\)
3: Initialize \(\hat{x}^{(1)}\) to white noise
4: While \(k\leq M\), do
5:\(\hat{X}^{(k)}\gets F\{\hat{x}^{(k)}\}\)
6:\(\hat{X}^{(k)}\leftarrow\left|\hat{X}\right|e^{j\angle\hat{X}^{(0)}}\)
7:\(\hat{x}^{(k+1)}\leftarrow F^{-1}\{\hat{X}^{(k)}\}\)
8:\(k\gets k+1\)
9: End while
```

**Algorithm 1** LSE-ISTFTM

## 3 Simulation Experiment

### Experimental Conditions

The experiment was performed on a PC with a Core i5 3.2 GHz processor and 4 G memory, using the MATLAB 2013a simulation software. To verify the effectiveness of the proposed algorithm, we used 100 sentences that had been recorded in a quiet environment. There were 10 speakers (five females and five males), each with 10 sentences, covering five subjects such as stock market, catering, tourism, sports and film. The length of each sentence was approximately 2 s, with a sampling rate of 8 kHz and a precision of 16 bit. The frame segmentation was performed on the signals, with a frame length of 512 sampling points and an interframe overlap of 50%, three frames of whispered speech and one frame of normal speech constituted a joint feature vector. We randomly selected 90% whispered speech sentences and the corresponding parallel corpus as training data, the rest (10%) was used as test data. The model does not consider speaker relevance. Because the speech information of the current frame of speech has a close relationship with the frame before and after the current frame, to achieve better conversion effectiveness, we not only used the current speech frame after DTW but also considered the frames before and after the speech frame. Also, under the condition that the pronunciation is standard Chinese, if the training set and test set are different subjects, even unseen speaker, it has little impact on the final result. To verify the effectiveness of the proposed L1/2 algorithm, we compared it with the L2 algorithm; the results are shown in Figure 2, which the number of EM iterations is 300. The data in Figure 2 show that the effectiveness of the proposed algorithm on speech reconstruction has been greatly improved compared to that of the L2 algorithm. We generated the spectrograms of the two algorithms after the inversion to further validate the advantages of the proposed method, as shown in Figure 3.

The data in Figure 3 show that compared to the L2 algorithm, the reconstructed speech using the proposed algorithm was clearer, with reduced interference from noise. The proposed method obtained the spectrograms similar to the reference normal speech without estimating the fundamental frequency. The harmonic component can be clearly seen from the spectrograms, indicating that the proposed method can obtain the spectrograms estimation of normal speech. We thus performed subsequent experiments using the proposed algorithm. Figure 3: Comparison of the spectrograms of two algorithm: (**a**) original speech; (**b**) L2 algorithm; (**c**) proposed algorithm. Figure 2: Experimental comparison of the L2 and L1/2 methods with different iteration numbers in speech inversion.