## 3 Methodology
### Experimental Setup  
**Baseline CSR System**: For our experiments, we use the conformer architecture, which combines convolution neural networks and transformers to model both local and global dependencies, respectively [63; 64]. We use the ESPnet toolkit [19] to run the experiments [65]. We train separate E2E systems for each of the three languages, i.e., Dutch, German, and Mandarin, using the adults' speech of the respective languages, and test the systems on their respective adults' and children's speech test sets. All of the audio files are singlechannel and recorded at a 16 kHz sampling rate. The training configuration of the baseline E2E model uses 80 dimensional log-mel filterbank features with 3-dimensional pitch features. The experiments were carried out till 20 epochs. For training the Dutch and German ASR systems, we use byte pair models with 5000 and 1000 unigram tokens, respectively. Since Mandarin is not an alphabetic language, the Mandarin ASR system instead uses a dictionary with \(\sim\)6 k characters. The non-language symbols (speaker filler, laugh, and unknown) are only available for the Dutch language and are thus only used in the Dutch experiments. The Mandarin and German databases mostly consist of read speech and are likely not to contain fillers (which are also not annotated). To evaluate the performance of our models, we compare them to a state-of-the-art pre-trained models, the Open-AI Whisper models [66]. Detailed results are provided in Appendix A. In short, for adults' speech, our model outperformed Whisper small, medium, and large despite not using a language model, for all three languages, except for German, where Whisper large outperformed our model, and Mandarin where Whisper medium outperformed our model. Hence, we carry out our experiments with the conformer model. **Augmentation and Normalization Experiments**: To study the effect of augmentation and normalization, three experiments were carried out:  
_Experiment 1: Augmentation_First, the adults' speech of each of the three languages was perturbed using SP. For each language, the perturbed adults' speech, combined with the original adults' speech, was then used to retrain the respective baseline models, after which these \"SP-augmented\" models were retrained with SpecAug applied during training (SP + SpecAug). The SP and SP + SpecAug models were tested on the children's speech of the respective languages; note that no changes were made to the audio signal of the test sets. This scenario is depicted in Figure 0(b). _Experiment 2: Normalization_The Effect of VTLN:_ For each language, we train a VTLN model on only the adults' speech. VTLN training does not require any transcriptions of the speech data. Since children's speech data without transcriptions is (more) often readily available (than with transcriptions that are often challenging to obtain), we add an experiment where the VTLN models are trained on (untranscribed) children's speech. Table 5 provides an overview of the trained VTLN models and the type of data they were trained on. VTLN is implemented during the feature extraction process as follows: during the training process of the ASR, the adults' speech training set features are normalized using the estimated VTLN factors obtained with the VTLN model trained on adults' speech or the VTLN model trained on children's speech, as indicated in Table 5. ASR models (following the baseline set-up) are then trained with these normalized features, one new ASR model for each VTLN model (i.e., three for Dutch and two for both German and Mandarin). This training scenario is depicted in Figure 0(b). During test, the features of the adults' and children's speech test sets are extracted and normalized to avoid any mismatch between the training and testing acoustic features and subsequently passed through the ASR system for decoding. This testing scenario is depicted in Figure 0(c).