## 2 Objective Evaluation Test
### Direct Signal Test  
Criterion: The remaining amount of direct signal in the surround channels of the stereo-to-multichannel upmix could result in undesired virtual sound sources, which could interfere with the spatial representation of sound events true to original. Although it could lead to a higher subjective perceived spatial quality, the remaining amount of direct signal in the surround channels would be against the assumptions made for upmix algorithms, and should therefore be as low as possible.  
Again, a special test signal is defined and used as input signal for the tested upmix algorithm. Different direct signals were taken from the database MedleyDB [12]. These audio recordings were then convolved with room impulse responses and mixed to a test signal (see Appendix A). The procedure of the direct signal test is shown in Figure 4.  
Figure 3: Panning test—angle of the virtual test sound sources compared with the determined virtual sound sources of the upmix algorithms: (**a**) algorithms upmix 1(a) and 1(b); (**b**) algorithms upmix 2(a) and 2(b).  
The generated surround channels \(x_{SL}\) (surround left) and \(x_{SR}\) (surround right) of the upmix are analyzed by determining their remaining amount of direct signal \(\hat{S}_{A}\). This is compared with the known test signal \(S\) and serves as the basis for evaluation. The score of the direct signal test  
\[score_{DT}=1-\frac{1}{N}\cdot\frac{1}{K}\sum_{n=1}^{N}\sum_{k=1}^{K}\frac{ \hat{S}_{A,env}(n,k)}{S_{env}(n,k)} \tag{6}\]  
is calculated from the mean of the quotient of the spectral envelopes [13]\(\hat{S}_{A,env}\) and \(S_{env}\) of the amounts of direct signals, across all \(N\) times and \(K\) frequencies, representing their relative deviation. To ensure a comparative evaluation, the summed power of the extracted surround channels must be equivalent to the summed power of the input signals. That is because signals before and after the upmixing process are considered. Only through using normalized surround signals is a comparative evaluation possible. This ensures, among others, that surround signals are considered correctly, which are identically equal to the input signals but reduced in power. That is because they would have the same relative amount of direct signal. The evaluation allows the comparison of the remaining surround channel direct signal with the known direct signal of the used test signal (see Figure 5).  
Upmix 1: Mode (a) contains a reduced remaining direct signal in the surround channels. Mode (b) contains a remaining direct signal which is slightly lower or greater.  
Upmix 2: The remaining direct signals are almost identical in modes (a) and (b), but slightly increased relative to the direct signal of the test signal. These proportionally increased remaining surround channel direct signals can occur because of input signal level adjustment or positive feedback of the upmix output signals. It should be noted that other upmix algorithms could also exhibit obviously reduced remaining surround channel direct signals.  
Figure 4: Block diagram: Direct signal test. Note that this is a simplified illustration of room impulse responses as a summary. See Appendix A for details of used room impulse responses and the calculation of \(x_{L}\) and \(x_{R}\). STFT: short-time Fourier transform.  
Figure 5: Direct signal test—remaining surround channel direct signal: (**a**) Algorithms upmix 1(a) and 1(b); (**b**) algorithms upmix 2(a) and 2(b). Note that the index \(n\) in the plots represents discrete values of time. \(|S(n)|\) represents the magnitude of the respective complex direct signal averaged over all frequencies.