# Spectral Envelope Transformation in Singing Voice for Advanced Pitch Shifting
## 6 Results and Discussion
### Objective Evaluation  
The objective evaluation provided satisfactory results. The NS measure described in the previous section allowed comparing the results of our scheme with Logic Pro X and PSOLA, quantifying the similarity between the spectral envelopes of the transformed samples and the corresponding original  
Figure 10: Continuous quality scale provided for the subjective evaluation.  
one, which defined the target of the transformation. Figures 11 to 13 show 95% confidence intervals with a notch at the median of each measure.  
The first parameters to be measured were the magnitude and phase of the harmonic peaks. Figure 11 shows the NS of the magnitude and phase of the first 10 harmonic peaks with respect to the envelope target. In general, the NS of the magnitude of the peaks was mostly similar among all of the pitch shifting schemes, but the mean of the first peak is slightly better adjusted to the target by using FDPS. This peak is under the fist formant, which presented a clearer transformation tendency, as shown in Section 3.2.1, and it is the most predominant one. From our point of view, the rest of the peaks do not provide any clue on the difference of the performance of the three schemes; anyway, their relative importance with respect to the lower peaks diminishes with the peak number. Regarding the phase of the harmonic peaks, the results were also very similar for the three schemes.  
The similarity of the central frequency and the bandwidth of the formants was measured, as well. Figure 12 shows the results of the NS parameter for the central frequency of the formants for both the harmonic and residual component. The average of the NS measurements indicates that the \(F3\) of the harmonic component achieved a 35.6% better estimation with Logic Pro X than FDPS, whereas the more dominant \(F1\) and \(F2\) formants were 34.5% and 12%, respectively, more accurately adjusted with FDPS. In the residual component, the mean NS of \(F2\) and \(F3\) was, respectively, 18.6% and 32.5%, closer to the target with FDPS than with Logic Pro X. The mean NS for \(F1\) was similar in these two cases. However, observe that the median (shown in the figures) and the shape of the distributions suggests a trend to a higher score with our approach also in this evaluation. In both components, PSOLA achieved the worst results.  
Finally, the results regarding the formant bandwidths are shown in Figure 13. Again, the mean of the NS results, for both the harmonic and residual components, indicate that our FDPS scheme attained better performance (larger mean NS) in the two first formants (\(B1\) and \(B2\)) than Logic Pro X and PSOLA. Moreover, the most significant difference appears in the bandwidth of the first formant, which highlights the better performance of our scheme.  
Figure 11: Normalized similarity (NS) of the 10 first harmonic peaks. (**a**) Magnitude of the peaks; (**b**) phase of the harmonic peaks.  
Figure 12: Normalized similarity of the central frequency of the first three formants. (**a**) Harmonic component; (**b**) residual component.  
Figure 13: Normalized similarity of the bandwidth of the first three formants. (**a**) Harmonic component; (**b**) residual component.