Formant analysis, the study of vocal tract resonances, is increasingly used beyond phonetics, in fields like behavioral science to investigate phenomena such as acoustic size exaggeration and articulatory abilities in animals. Estimating VTL acoustically and producing scale-invariant formant representations are crucial steps in this research. However, existing literature on speaker normalization is often highly technical and lacks simple guidelines and readily available tools, particularly for non-phonetic applications. This paper aims to bridge this gap by providing up-to-date, accessible solutions for measuring and verifying formant frequencies, estimating VTL, and extracting size-invariant formant patterns, especially in situations where linguistic content cannot be perfectly controlled.

The paper reviews existing literature on formant analysis and speaker normalization, highlighting the limitations of previous approaches, especially regarding their applicability to non-speech vocalizations and diverse research contexts beyond human speech. It mentions the extensive but often technical nature of existing speaker normalization methods, the lack of consensus on optimal methods for different contexts, and the scarcity of user-friendly tools. The authors specifically address the need for a guide tailored to researchers in fields like psychology and animal behavior, who may not have a background in phonetics.

The paper outlines a step-by-step methodology for formant analysis, beginning with formant measurement using linear predictive coding (LPC). It emphasizes the importance of manual verification and correction of LPC estimates due to their inherent error-proneness, especially in high-pitched and noisy vocalizations. The authors introduce `formant_app`, an open-source software solution integrated into the R package `soundgen`, which provides an interactive environment for formant annotation and correction with visual and auditory feedback. Two primary approaches to speaker normalization are detailed: intrinsic and extrinsic methods. Intrinsic methods, using a single recording, involve calculating formant ratios and geometric means to obtain a scale-invariant representation. The `estimateVTL` function, implementing a regression method, calculates apparent VTL based on a single-tube model, with residuals providing a scale-invariant vowel space. Extrinsic methods, using multiple recordings, offer more accurate estimates of speaker- and vowel-specific scale factors through averaging or mixed models. The paper provides R code examples illustrating these methods. The paper also contrasts linear and logarithmic formant representations. Linear representation is suitable for voice production studies, while logarithmic representation, using base-two logarithms or perceptual units like mels or barks, is better aligned with auditory perception and reveals formant ratio invariance across speakers. The `normalize` function in the `phonTools` package provides an R implementation for log-mean normalization. The use of multilevel Bayesian models for estimating speaker-specific scaling factors is also discussed, using the `brms` package in R.

The authors find that manual verification of formant measurements significantly improves accuracy. Both intrinsic and extrinsic speaker normalization methods are effective, with extrinsic methods (using multiple recordings) yielding more accurate results, especially for VTL estimation. They demonstrate that the regression method for VTL estimation, implemented in `estimateVTL`, is robust to missing data and provides both VTL estimates and scale-invariant vowel representations. The use of upper formants (F3 and F4) is crucial for accurate VTL estimation, even when lower formants are missing or unreliable. Logarithmic methods for intrinsic normalization show better generalization beyond the training VTL range. Multiple estimates of apparent VTL per speaker show high correlation across different estimation methods (eVTL, mean log-formant, and scale factor k from mixed model K1). However, differences in VTL across vowels within a speaker are significant and highlight the challenge of estimating true anatomical VTL from a single vocalization of an unknown vowel. Extrinsic normalization methods, which leverage multiple vowels per speaker, significantly improve the prediction of perceived speaker size. Intrinsic normalization, while less accurate for VTL estimation, performs reasonably well in vowel separation when using sufficient formants. The authors analyze different scenarios illustrating the application of the presented methods for various research questions, emphasizing the importance of controlling vowel quality when comparing VTL across conditions.

The findings highlight the importance of combining accurate formant measurement with appropriate statistical methods for reliable VTL estimation and scale-invariant formant pattern analysis. The choice between intrinsic and extrinsic normalization depends on the research question and data availability. The authors demonstrate that while different methods provide comparable results when comparing speaker-typical VTL across a range of vowels, discrepancies arise when analyzing vowel-specific VTL variations. The use of multiple vowels per speaker significantly improves VTL estimation and the prediction of perceived speaker size, mirroring human listener capabilities. The study emphasizes the need for careful consideration of vowel quality when interpreting VTL differences across conditions.

This paper provides a valuable resource for researchers interested in calculating VTL and extracting scale-invariant formant patterns from speech and non-speech vocalizations. It emphasizes the critical role of manual formant verification and the advantages of using extrinsic normalization methods when comparing VTL across conditions. Future research should focus on developing improved methods for intrinsic VTL estimation that account for vowel-specific variations and better approximate human perceptual abilities. Extending these methods to handle more complex vocal tract configurations is also a key area for future development.

The study's reliance on existing datasets limits the ability to validate VTL estimates against anatomical ground truth. The single-tube model for VTL estimation may not be perfectly applicable to all vocalizations, particularly those with complex vocal tract shapes. The generalizability of the findings to non-human species with significantly different vocal tract morphologies needs further investigation. While the authors account for certain limitations in their analyses and interpretations, there is always the possibility that unforeseen factors could affect the results.