Extracting cepstral coefficients and derivatives

The extraction of cepstral information consists of seven steps. These steps, with the exception of step four, are identical for MFC and LPC analysis. This process is

visualised, for MFC analysis, in Figure 3.12.

The entire speech sample is initially divided into frames based on a window size of

x(ms), shifted across the sample at intervals ofy(ms). Typically, either a rectangular or hamming window is used for this. In this thesis a hamming window was used. A

pre-emphasis filter is then applied to the signal using the first order difference equation:

s0_n =sn−ksn−1 (3.13)

from Younget al.(2006: 62)

16_{The abbreviations used here are the same as those used in the HTK toolkit documentation (Younget}

wheresn(n=1,2,3. . . n) is the signal from a given frame andk is the pre-emphasis

coefficient. The pre-emphasis filter accounts for the spectral tilt by increasing the

amplitude of lower intensity, high frequency components relative to the amplitude of higher intensity, low frequency components.

Figure 3.12: Visual representation of extraction of cepstral (in this case MFC) informa-

tion from a speech signal (Jurafsky 2007)

At step three, the signal from each frame is converted to a power spectrum by applying

a Discrete Fourier Transform (DFT) and a filterbank is then applied. The filterbank consists of a number of triangular filters applied across the entire frequency range. At

this stage, the processes of analysing the MFC and LPC differ slightly. For the MFC, the filterbank is based on the Mel-frequency scale; a perceptual scale which captures the

non-linearity of the human auditory system (Johnson 2008). The relationship between linear frequency (f) and Mel-frequency (m) can be expressed as (Figure 3.13):

m= 2595log10 1 + f 700 (3.14) from O’Shaughnessy (1987)

In the case of the MFC, the filterbank consists of filters whose width and absolute degree of overlap increases with frequency (Figure 3.13). For the LPC, the filterbank is

applied to the linear frequency scale (i.e. with no transformation of the power spectrum), involving filters of equal width and absolute and proportional overlap. The energy in

each filter is then summed and, in step five, the values logged. The penultimate step, involves fitting a discrete cosine transform (DCT) to the logged filterbank energies. The

Figure 3.13: Relationship between linear and Mel frequency scales

The final stage involves extracting derivatives based initially on the vectors of CCs for

adjacent frames. Deltas (Ds) are calculated by:

Dt= N P n=1 n(ct+n−ct−n) s N P n=1 n2 (3.15) where: Dt= Delta coefficient t= Frame

ct+n, ct−n= Static CCs from adjacent frames

from Younget al.(2006: 62)

Delta-deltas (As) are calculated by applying Equation 3.15 to the Ds rather than the CCs.

Figure 3.14: Graphical representation of the Mel (above) and linear frequency (below)

filterbank applied to the power spectrum from a given window, with 50% overlap between filters (from Lei and Lopez-Gonzalo 2009: 2324)

3.4

Limitations

There are a number of general limitations with the experiments in this thesis. Firstly, across all experiments LRs are computed using contemporaneous data from single

sample per speaker, i.e. divided in half to compute SS comparisons. This is due to the fact that databases with non-contemporaneous samples (i.e. two recordings

per speaker separated by some period of time) generally do not contain sufficient numbers of speakers from the narrowly defined sociolinguistically groups relevant

to the experiments in this thesis. Secondly, the ONZE, NE and PVC datasets were collected primarily for sociolinguistic research and are therefore liable to the limitations

outlined in §2.4.2.1. For TIMIT, the level of forensic relevance is further limited by the use of read speech (the preference for TIMIT over other ASR databases is explained

in Chapter 6). All of the samples used were also recorded directly, and most in high quality and digitised with optimum sampling rates.

It is predicted that the use of contemporaneous, high quality samples will lead to overly optimistic performance compared with real forensic conditions. The potential

as highlighted in §2.2.5, relatively little work has empirically tested the impact of non-contemporaneity on the outcome of numerical LRs (with the exception of Enzinger

and Morrison 2012 and Coe 2012). Furthermore, given that little work has considered the research questions of this thesis, it is considered preferable to test these questions

initially using optimal data. This will help to reveal the specific effects of variability in the definition of the relevant population and sample size in LR-testing, without

the confounding issues of various sources of mismatch between suspect and offender samples encountered in forensic casework.

In Chapters 4 and 5, a combination of intrinsic and extrinsic testing (§3.2.2.2) was used. This may exaggerate the differences in LR output between the regionally Matched

and Mixed/Mismatched sets, since intrinsic testing predicts greater similarity between datasets extracted from the same database. The use of auto-generated data in Chapters

4 and 8 is also a substantial limitation, since the accuracy of segmental boundaries is reduced for forced-aligned TextGrids. Further, the procedures implemented to correct

and remove errors serve to identify clear outliers, rather than more subtle measurement errors (although the use of parametric representations of the trajectories does help

to reduce the noise in the raw data) or errors due to incorrect segmental boundaries. Further experiment-specific limitations are also discussed in the relevant data chapters.

Regional Background: /u:/

This chapter explores the extent to which LRs are affected by different definitions of the relevant population with regard to regional background, using the formant trajectories

of /u:/ as input. Firstly, LRs were computed using multiple sets of regionally defined test data and a single set of reference data, where one test set matches the reference set

for regional background. Secondly, calibrated LLRs for a single test set were computed using multiple systems containing: (a) regionallyMatcheddevelopment and reference

data and (b) regionallyMixeddevelopment and reference data.

4.1

Introduction

As outlined in §2.3.1, logical relevance based on offender language and sex has been the preferred approach for defining the relevant population in the vast majority of LR-based

research and casework. However, a substantial issue for the application of logical relevance to FVC is the extent to which analysts’ decisions relating to these sources of

between-speaker variation affect LR output. This chapter presents the results of two experiments which address this issue by considering different definitions of the relevant

population with regard to regional background using the formant trajectories of /u:/ (GOOSE; Wells 1982) as input.

In Experiment (1), LRs were computed using a single set of regionally homogeneous reference data and multiple sets of regionally defined test data, where one matches the

reference data for dialect. This experiment reflects the practical issue in LR-based FVC of the limited availability of databases for assessing typicality. Therefore, in the vast

majority of cases the analyst would currently need to use reference data (forensic or non-forensic; §2.4.2) which displays some degree of mismatch with the offender in

terms of the regional background of the reference speakers. Experiment (1) compares the effects of such mismatch on LR output relative to a set of appropriate reference

data.

Experiment (2) relates more directly to analyst decisions regarding the relevant popu-

lation. LR scores were computed for a set of regionally homogeneous test data using systems which represent different controls over regional background. Since the defi-

nition of the relevant population in casework informs the choice of speakers used as development and reference data, the effects on LR output are considered across both

the feature-to-score (§3.2.2) and score-to-LR (§3.2.4) stages. The systems are defined as (a)Matched: using development and reference speakers who match the test data

for regional background, reflecting a situation where the analyst defines the regional variety of the relevant population narrowly and correctly relative to the offender, and (b)

Mixed: using speakers from different regional varieties as development and reference

data, reflecting limited control over regional background. The Mixed condition is, to

some extent, consistent with Rose (2004) where regional background is defined broadly aslanguage.