## 5 Results
### Frequency-Domain Behavior
The ANMR has been previously researched as a perceptually-informed measure to evaluate the audibility of aliasing distortion [41, 65]. The algorithm computes the power ratio in decibels between the wanted harmonics and aliased components, but takes into account the masking effects of the former. An A-weighting filter is applied to all signals prior to the evaluation of the ANMR in order to account for the frequency-dependent sensitivity of hearing for low-level sounds. Signals with an ANMR value below \(-10\,\mathrm{dB}\) are considered to be completely free from perceivable aliasing. A detailed account of this method can be found in [65]. Figure 15a compares the measured ANMRs for a set of sinusoidal inputs with fundamental frequencies between 1 and 5 kHz processed by the Lockhart model at different sampling rates. The ideal alias-free signals required to compute these values were synthesized using Fourier analysis and additive synthesis, as suggested in [41]. All signals were downsampled back to audio rate (i.e., 44.1 kHz) prior to evaluation. A dashed horizontal line has been used to indicate the \(-10\,\mathrm{dB}\) hearing threshold for aliasing distortion. In Figure 15a we can observe the significant increase in  
Figure 14: Spectrogram for a 1 V linear sweep from 20 Hz–5 kHz processed with the proposed Serge wavefolder model: (**a**) at audio rate; (**b**) using two times oversampling; (**c**) with antialiasing at audio rate; and (**d**) with antialiasing and oversampling by two. Figure 13: Spectrogram for a 1 V linear sweep from 20 Hz–5 kHz processed with the proposed [PERSON] wavefolder (\(R_{\mathrm{L}}=50\,\mathrm{k}\Omega\)) model: (**a**) at audio rate; (**b**) using two times oversampling; (**c**) with antialiasing at audio rate; and (**d**) with antialiasing and oversampling by two. signal quality obtained by the proposed antialiasing method when applied to the Lockhart wavefolder, even when operating at audio rate. Moreover, these measurements show that the performance of the proposed method, when combined with two-times oversampling, is on par with oversampling by a factor of 8. For all fundamental frequencies below approximately 4.2 kHz, the ANMR lies below the \(-10\) dB line. This range can be regarded as sufficient for musical applications if we consider that the highest fundamental frequency on a standard grand piano is 4186.01 Hz (MIDI note C8). Figure 15b shows the measured ANMRs for the Serge wavefolder. When implemented at audio rate, the output is free from perceivable aliasing for fundamental frequencies up to approximately 2 kHz. These measurements go in accordance with the Spectrogram in Figure 14a, which shows aliasing is significantly more evident above this frequency. The use of the antiderivative method yields results comparable to those of oversampling by a factor of two, with all measured fundamental frequencies below approximately 4.6 kHz lying below the \(-10\) dB aliasing threshold. Overall, these results indicate the proposed Serge wavefolder model can operate at audio rate with the help of the antiderivative method, therefore avoiding the need for oversampling.