# Audio Time Stretching Using Fuzzy Classification of Spectral Bins
## 4 Evaluation
This is also reflected in the results of the _Vocals_ excerpt, where the proposed method also performed well, while scoring slightly lower than HP. For the _Techno_ sample, the proposed method scored significantly higher than \begin{table}
\begin{tabular}{l l} \hline \hline
**Name** & **Description** \\ \hline CastViolin & Solo violin and castanets, from [37] \\ Classical & Excerpt from _Bolero_[PERSON] performed by the _London Symphony Orchestra_ \\ [PERSON]\(\mathrm{[PERSON]}\) & Excerpt from _Cocaine_[PERSON] performed by _[PERSON]_ \\ DrumSolo & Solo performed on a drum set, from [37] \\ Eddie & Excerpt from _Early in the Morning_, performed by _[PERSON]_ \\ Jazz & Excerpt from _I Can See Clearly_, performed by the _Holly Cole Trio_ \\ Techno & Excerpt from _Return to Balojax_, performed by _Deviant Species and Scorb_ \\ Vocals & Excerpt from _Tom’s Diner_, performed by _[PERSON]_ \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of audio excerpts used in the subjective listening test. the other methods with TSM factor \(\alpha=1.5\). For TSM factor \(\alpha=2.0\), however, the proposed method scored lower than EL. The proposed method also scored highest for the _JJCalc_ sample with TSM factor \(\alpha=2.0\). The proposed method performed more poorly on the excerpts _DrumSolo_ and _Classical_. Both of these samples contained fast sequences of transients. It is likely that the poorer performance is due to the individual transients not being resolved during the analysis, because of the relatively long analysis window used. Also, for the excerpt _Eddie_, EL scored higher than the proposed method. Note that the audio excerpts were not selected so that the results would be preferable for one of the tested methods. Instead, they represent some interesting and critical cases, such as singing and sharp transients. The preferences of subjects over the tested TSM methods seem to depend significantly on the signal being processed. Overall, the MOS values computed from all the samples suggest that the proposed method yields slightly better quality than HP and practically the same quality as EL. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**\(\alpha\)= 1.5**} & \multicolumn{3}{c}{**\(\alpha\)= 2.0**} \\  & **PV** & **HP** & **EL** & **PROP** & **PV** & **HP** & **EL** & **PROP** \\ \hline CastViolin & 1.8 & 3.8 & 3.6 & **4.1** & 1.4 & 3.6 & 3.3 & **4.1** \\ Classical & 2.3 & 3.5 & **3.7** & 3.3 & 1.6 & 3.0 & **3.7** & 2.8 \\ JJCalc & 2.7 & 2.5 & **3.4** & 2.9 & 1.2 & 2.5 & 3.1 & **3.2** \\ DrumSolo & 1.5 & **3.5** & 3.2 & 2.3 & 1.7 & 2.4 & **2.5** & 1.8 \\ Eddie & 1.9 & 3.1 & **4.2** & 3.2 & 1.2 & 2.2 & **3.6** & 3.1 \\ Jazz & 1.9 & **3.6** & 3.4 & **3.6** & 1.5 & 3.3 & 2.7 & **3.7** \\ Techno & 1.3 & 2.7 & 3.3 & **4.1** & 1.6 & 2.5 & **3.1** & 2.7 \\ Vocals & 1.7 & **3.5** & 2.9 & 3.4 & 1.5 & **3.3** & 2.7 & 3.1 \\ \hline Mean & 1.9 & 3.3 & **3.5** & 3.4 & 1.5 & 2.9 & **3.1** & **3.1** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean opinion scores for the audio samples. PV: phase vocoder; HP: harmonic–percussive separation; EL: élastique algorithm; PROP: proposed method. Figure 8: _Cont._  
The proposed method introduces some additional computational complexity when compared to the standard phase-locked vocoder. In the analysis stage, the fuzzy classification of the spectral bins requires median filtering of the magnitude of the analysis STFT. The number of samples in each median filtering operation depends on the analysis hop size and the number of frequency bins in each short time spectra. In the modification stage, additional complexity arises from drawing pseudo-random values for the phase randomization. Furthermore, computing the phase randomization factor, as in Equation (13), requires the evaluation of two hyperbolic tangent functions for each point in the STFT. Since the argument for the second hyperbolic tangent depends only on the TSM factor, its value needs to be updated only when the TSM factor is changed.