# Evaluation of Glottal Inverse Filtering Techniques on
## 3 Experiments
### GIF Parameter Tuning  
Each of the evaluated GIF methods considers several parameters that should be fine-tuned to obtain the optimal results. During the first phase of the analysis methodology, grid-search optimisation was conducted for each method and speech signal in the dataset, driven by the median absolute waveform error (MAE-Wave) as the optimization error metric (see Figure 1). This metric is computed by averaging the root-mean-square (RMS) error between the normalised estimated glottal flow and the ground truth across all the speech signal periods [30]. This normalisation is twofold, consisting, first, of a time alignment by peak-picking the autocorrelation against the ground-truth glottal flow. Secondly, it is normalised pulse-by-pulse using the GCIs as time marks by applying a scale and the DC offset normalization factors obtained by minimising the total squared error between the ground truth and the estimated glottal flow.  
Table 14 presents the GIF methods and the parameters explored in the previous literature. The parameter ranges used in the present work were chosen accordingly. Furthermore, none of the reviewed studies included an analysis of all the IAIF and QCP variants.  
As mentioned in Section 2, there are two common parameters for all methods that must be defined: the vocal tract order \(N_{v}\) and the lip radiation coefficient \(d\). Following [PERSON] and [PERSON]'s study [25], the \(N_{v}\) coefficient ranged from \([Fs/1000]-2=6\) to \([Fs/1000]+6=14\) with increments of 1, which is sufficient for modeling vowel vocal tract resonances. Moreover, the \(d\) coefficient varied from 0.8 to 0.99, with increments of 0.01. Furthermore, IAIF, IOP-IAIF, and GFM-IAIF also had the glottal source order (\(N_{g}\)) parameter. For the first two methods, a range from 3 to 6 with increments of 1 was considered, whilst in the case of the GFM-IAIF method, it was fixed at 3 according to [PERSON] and McLoughlin definition [25]. In addition, for IAIF and IOP-IAIF, the HPF activation was also considered as an optimisation parameter. Lastly, the parameters of the QCP, based on [PERSON] et al. [28], ranged as follows: \(DQ\) from 0.4 to 1 with a step of  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \(N_{v}\) & \(N_{g}\) & \(d\) & **HPF** & **DQ** & **PQ** & **RQ** & **ST** \\ \hline IAIF & 6:1:14 & 3:1:6 & 0.8:0.01:0.99 & 0/1 & & & & \\ IOP-IAIF & 6:1:14 & 3:1:6 & 0.8:0.01:0.99 & & & & & \\ GFM-IAIF & 6:1:14 & 3 & 0.8:0.01:0.99 & 0/1 & & & & \\ GCP & 6:1:14 & 3:1:6 & 0.8:0.01:0.99 & & 0.4:0.05:1 & 0:0.025:0.2 & 0.0 & 0.05:0.2 & 1 \\ ST-QCP & 6:1:14 & 3:1:6 & 0.8:0.01:0.99 & & 0.4:0.05:1 & 0:0.025:0.2 & 0.0 & 0.05:0.2 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters tuned for each GIF method evaluated. Vocal tract order is referred to as \(N_{v}\), glottal source order as \(N_{v}\), and lip radiation as \(d\), HPF represents a high-pass filter flag, DQ, PQ and RQ denote duration, position and ramps quotient, whilst ST stands for the spectral tilt compensation binary flag. The ranges are written as initial valueincrement:final value.  
0.05, \(PQ\) from 0 to 0.2 with a step of 0.025, and \(RQ\) from 0 to 0.2 with a step of 0.05. Table 1 summarizes all the parameter ranges and values for each GIF method.