The sub-band cepstrum as a tool for local spectral analysis in forensic voice comparison (2023)

Abstract: This paper exploits band-limited cepstral coefficients (BLCCs) in forensic voice comparison (FVC), with the primary aim of locating speaker-sensitive spectral regions. BLCCs are sub-band cepstral coefficients (CCs) which are easily obtained by a linear transformation of full-band CCs. The transformation gives the flexibility of selecting any sub-band region without the recurrent cost of spectral analyses. Using multi-band BLCCs obtained by sliding a 600-Hz sub-band every 400 Hz across the full [0-5kHz] range, FVC experiments were attempted using citation recordings of the 5 Japanese vowels from 297 adult-male, native speakers. The FVC results give locations and ranges for the most speaker-sensitive sub-bands, and show that combining 3-4 of these yields comparable FVC performance with full-band CCs. Owing to their ability to easily extract locally-encoded speaker information from full-band CCs, it can be conjectured that BLCCs have a significant role to play in the search for meaningful interpretations of the numerical outcome of forensic analyses.

## introduction in forensic voice comparison (fvc), the forensic scientist typically needs to compare a pair of speech recordings: the source-questioned and source-known samples, and to obtain the strength of evidence quantified by a likelihood ratio (lr). for this purpose, it has become standard practice to parameterise the acoustic speech signal using low-dimensional vectors of cepstral coefficients (ccs). these are automatically extracted from any phonetic segments, and have been shown to be effective for speech and speaker classification. the effectiveness is attributable to the ability of lowordered ccs to produce cepstrally-smoothed spectra with reduced sensitivity to "noninformation bearing variabilities" @xcite and, thus, with increased distinctiveness. such spectra may be obtained with full-band ccs which yield spectral representations over the full frequency range, or with sub-band ccs which give access to local regions within the full range. consistent with our long-term goal of interpreting the fvc outcome beyond numerical lr values, the present study focuses on sub-band ccs with the dual aim of (a) locating vowel spectral regions that are most sensitive to speaker differences, and (b) determining the extent to which such regions affect lr values compared to the full band from vowel to vowel. the motivation for this endeavour stems from an old premise @xcite : 151) that speaker information is not uniformly encoded throughout vowel spectra, i.e., there exist local regions of strong speaker and phonetic specificity. supportive evidence has since been reported in a wide range of studies (inter alia: @xcite @xcite @xcite @xcite @xcite . the presentation of our work is as follows. sec. 2 describes and illustrates the method (clermont 2022) adopted for obtaining sub-band ccs, hereafter referred to as band-limited ccs (blccs in short). the blcc method affords flexibility and efficiency, two properties exploited in this work. sec. 3 recalls the basics of the lr framework. sec. 4 concerns the multi-speaker vowel data used, the blcc parameterisation applied to a sequence of sub-bands, the fvc procedures, and the lrbased metric for performance assessment. sec. 5 presents full-band and sub-band fvc results for each vowel. sec. 6 discusses the results in context of previous work, and sec. 7 outlines potential ways forward. ## the blcc method this section focuses on the method employed for obtaining blccs by a linear transformation of fullband ccs. the method is described in sec. 2.1, and its mathematical formulation is outlined in sec. 2.2. in sec. 2.3, the numerical and spectral behaviours of blccs show that the practical size for a blcc vector depends on the fraction of the full-band's frequency range occupied by the sub-band's width. ## likelihood ratio framework the lr framework provides the theoretical foundation upon which voice evidence is analysed for source-inference purposes. in fvc, the task of the expert is to estimate the strength of voice evidence using the lr expressed as follows: the lr is the ratio of two conditional probabilities: the numerator is the probability (𝑝) of the evidence (𝐸) given the prosecution (samespeaker) hypothesis (𝐻 𝑝 ) , while the denominator is the probability given the defense (differentspeaker) hypothesis (𝐻 𝑑 ). the evidence ( 𝐸) typically consists of the source-questioned sample ( 𝑋 ) and the sourceknown sample (𝑌). in theory, the belief of the trierof-fact regarding the hypotheses, which was developed by the previously presented evidence, is to be updated by the lr; the assessment of the newly presented evidence. in other words, the belief of the decision maker regarding the suspect being guilty or not changes as a new piece of evidence is presented to them in the form of a lr. the further away from @xmath0, the more strongly the lr supports either of the competing hypotheses. ## experiment descriptions and results two fvc experiments were run separately per vowel, and the results are jointly charted in fig. 4 . in experiment 1, speaker information locallyencoded in the spectrum was investigated vowelby-vowel by conducting the experiments with the multi-band blccs (see the cllr values obtained for the 12 sub-bands are displayed as a red curve at the bottom plot of each panel included in in experiment 2, the sub-band lrs obtained from experiment 1 were fused from two to all subbands as per the following list (r) = {2,3,…,12}. all possible combinations of r sub-bands ( 12 𝑟 ) were also included. in the top plot of each panel, the best (lowest) cllr value is given for each r together with the cllr value of the single best sub-band (@xmath1. the cllr for the full-band ccs is indicated by the horizontal dotted line. the three best sub-bands (fused) are highlighted in blue in the bottom plot, and the three worst sub-bands (fused) are highlighted in pink. ## discussion the fvc results presented in sec. 5 confirm the existence of speaker-sensitive spectral regions, which principally agree with previous acoustic and articulatory studies of vowels. as such, it can demonstrably be argued that blcc is a useful analytical tool equipped with flexibility and precision in selecting any sub-band of interest. the formant frequencies (f1, f2 and f3) are common phonetic features in linguistic-phonetic fvc @xcite @xcite . the analytical potential of the multi-band blccs, however, unavoidably led us to notice that the regions corresponding to formant frequencies do not always contain strong speaker information. for example, the cllr values for sub-bands spanning the f1-f2 region of /i/, the f2 region /o/ and the f3 region of /a/ are relatively high compared to the other regions. this suggests that sub-band selection based strictly on formant ranges is an unnecessarily constraining and even sub-optimal solution. a case in point is @xcite results based on sub-band cepstral distances and on prior knowledge of fixed f1, f2 and f3 sub-bands. a set of fvc experiments was done with the sub-bands that were selected according to the fixed f1, f2 and f3 ranges provided in @xcite for the same experiments performed in the current study. the resultant cllr values are shown in the results from the 2 rightmost columns of notwithstanding this discrepancy for now, the trend of cllr values in the 2 middle columns of the results obtained in this study are based only on male speech samples. while this is practically justified because males tend to commit crimes more often than females, further experimentation is desirable with a wider variety of speakers. however, the analytical power of blccs should remain unaffected by gender or age. it is the locations and ranges of speaker-sensitive spectral regions that could differ with these factors. while retaining intrinsic properties of the cepstrum (e.g., ease of extraction, immunity to insignificant spectral details), the analytical power of blccs allows the forensic scientist to flexibly shift the focus of scrutiny and interpretation according to the selected sub-band region(s). this is an invaluable contribution that blccs can bring to the task of communicating the fvc outcome to the trier-of-fact in a more approachable way. ## future work the blccs exploited here are based on lp modelling of the speech signal and extracted on a linear frequency scale. however, there may be further insights to be gained by applying the same linear transformation to ccs from filter-bank outputs, combined with a nonlinear mapping of the frequency axis such as the often-used mel scale. it is interesting to note that, except for /i/, our bestperforming sub-bands include the lower-spectral regions that are precisely emphasised with mel-frequency ccs (mfccs). a deeper investigation of mfccs with differing sub-band widths and overlaps is therefore possible using our flexible approach to selecting local spectral regions. from a forensic point of view, it is coherent to extend the application of blccs to non-vowel sounds @xcite , whose speaker-sensitive spectral properties have received relatively less attention. from a linguistic point of view, it is conceivable that blccs could also be used as an ancillary or alternative parameter in the areas of acoustic-phonetics (e.g., efficient encoding of contrastive features as in iskarous (2018)) and socio-phonetics (e.g., exploration of accentspecific sub-bands) @xcite . in connection with these applications, it would be useful to study correlations between blccs and formant frequencies via the linear regression models developed by @xcite and @xcite , and recently explored by @xcite in the fvc context. finally, it is hoped that the sub-band approach embedded in blccs will bring new perspectives in other areas of speech science and technology, such as speech classification @xcite , spoofing detection @xcite , language identification @xcite , and speech emotion recognition. any pieces of information related to speaker variability, speech emotion, or synthesised speech, which are found to be notably encoded in specific sub-bands, would be advantageous for building robust classification systems, or for training deep-learning models. these technological pursuits are likely to benefit from the flexibility and efficiency afforded by the blcc approach to subband spectral analysis.