# Audlet Filter Banks: A Versatile Analysis/Synthesis Framework Using Auditory Frequency Scales
## 5 Evaluation
### Utility for Audio Applications  
#### 5.2.1 Method  
This experiment is an example application of the Audlet framework to audio source separation. Given a mixture of instrumental music and voice, we constructed various analysis-synthesis systems and separated the voice from the music. The systems were designed so as to assess the effects of perfect reconstruction, shape and bandwidth of the filter, and auditory scale on the quality of sub-channel processing at low, mid, and high redundancies. Four systems were implemented:  
**trev_gfb:**: a state-of-the-art gammatone FB with approximate reconstruction (the acronym **trev** stands for \"time reversal\"). The \(H_{k}\)'s followed (7) with \(w(\xi)=w_{c\text{s}CTA,1019}(\xi)\) (22) with a threshold \(\epsilon=10^{-5}\). The synthesis filters \(G_{k}(e^{2i\pi\xi})=\overline{H_{k}}(e^{2i\pi\xi})\). This corresponds to the baseline system used in audio applications like [11; 28; 29]. **Audlet_gfb:**: an Audlet FB with a gammatone prototype. The \(H_{k}\)'s were computed as in **trev_gfb** but the synthesis stage was Algorithm 1. This system aims to compare to the baseline system and assess the effect of perfect reconstruction. **Audlet_hann:**: an Audlet FB with a Hann prototype. This system aims to assess the effect of filter shape. **STFT_hann:**: an STFT using a 1024-point Hann window. Synthesis was achieved by the dual window [2]. The time step was then adapted to match the desired redundancy \(R_{\text{I}}\). This corresponds to the baseline system used in most audio applications (e.g., [10; 66]). This system aims to assess the use of an auditory frequency scale. The effect of filter bandwidth was assessed by varying parameter \(\beta\). Specifically, two values were tested: \(\beta\in\{1,1/6\}\). Using a value of \(\beta\
eq 1\) means a clear departure from auditory perception but may help better resolve spectral components, particularly at high frequencies where the auditory filters become really broad (see (6)). Accordingly, many audio applications that rely on constant-Q or wavelet transforms use 12 or more bins per octave (e.g., [46; 63]). The performance of all systems were evaluated at three redundancies: \(R_{\text{t}}\in\{1.1,1.5,4\}\). To this end, (15) was used with \(c_{bw}\) adjusted such that \(R_{\text{t}}\) was achieved. The quality of the separation was assessed by computing energy ratio- and perceptually-based objective measures according to [67]. Energy ratio measures include the signal-to-distortion ratio (SDR) and signal-to-artifact ratio (SAR). Perceptual measures include the overall perceptual score (OPS) and target perceptual score (TPS). OPS assesses the general audio quality of the separation, while TPS assesses the preservation of the target. All measures were computed using the PEASS toolbox [67]. The following parameters were fixed for systems trev_gfb, Audlet_gfb and Audlet_hann: \(f_{s}=22.05\) kHz, \([f_{\text{min}},\,f_{\text{max}}]=[20,10,000]\), Scale = ERB, and \(K\) = 209 filters corresponding to \(V=6\) filters/ERB. The signal mixture, shown in Figure 4(a), was created by adding an instrumental music signal to a singing voice signal (target), shown in Figure 4(b). The separation was performed by analyzing the mixture with the analysis FB, applying a binary TF mask to the sub-band components by point-wise multiplication, and computing the output signal from the modified sub-band components using the synthesis stage. This operation corresponds to the application of a frame multiplier in signal processing [9; 68]. In order to create the binary masks, the target signal was analyzed by the FB and the magnitude of the coefficients was hard thresholded with a threshold of \(-25\) dB. The threshold value was varied between \(-40\) and \(-20\) dB in 5-dB steps. While the threshold value did affect the separation performance, all configurations were affected equally. The value of \(-25\) dB was selected because it yielded good separation results for both the gammatone and Hann prototypes.