Normalize Vowels

Description

Function to normalize vowels using one of several methods.

Usage

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normalize(formants, speakers, vowels, method = 'neareyE', 
          corners = NULL)

Arguments

formants

A matrix or dataframe containing formant frequency information for vowels. Each row is assumed to indicate data from a single vowel. At least two columns (indicating information regarding at least two formants) are required.

speakers

A vector indicating which speaker produced each vowel in 'formants'. The length of this vector must equal the number of rows in 'formants'.

vowels

A vector indicating the vowel category of each vowel in 'formants'. The length of this vector must equal the number of rows in 'formants'.

method

A string indicating the desired method. Choices are 'neareyE', 'neareyI', 'lobanov' and 'wandf'. See details for more information.

corners

For the 'wandf' method, a vector of two strings indicating the lowest F1-highest F2 vowel, and the highest F1-intermediate F2 vowel for the vowel system. In most vowel systems these are an /i/-like vowel, and an /a/-like vowel, respectively. Vowels must be provided in that order.

Details

This function normalizes vowels based on provided formant frequencies (FFs). The available methods are:

Nearey formant-extrinsic log-mean ('neareyE'): This method finds the logarithmic-mean FF across all vowels produced by a speaker, and subtracts this value from the log-transformed FFs representing each vowel.

Nearey formant-intrinsic log-mean ('neareyI'): This method finds the logarithmic-mean for each formant independently across all vowels produced by a speaker. The log-mean for each individual formant is then subtracted from the log-transformed FF representing each vowel.

Lobanov ('lobanov'): This method finds the mean and standard deviation for each formant. FFs are then standardized (in the statistical sense) using these estimated parameters for each speaker, for each formant.

Watt and Fabricius ('wandf'): This method requires the user to provided point vowels representing the frontmost and highest vowel, and the lowest (and, ideally central) vowel in a vowel system. An estimate of the centroid of the vowel system is calculated based on these values. Normalized FFs are then expressed as the ratio of observed FFs to the estimated centroids, independently for F1 and F2.

For both Nearey methods, and the Lobanov method, the average is found for each vowel category within-speaker before calculating the overall mean. As a result, the data from each speaker may contain unequal numbers of each vowel category. However, all speakers must be represented by the same vowel categories or the result will be (possibly) subtle differences in normalized vowel spaces dues to the possibly differing estimates of means and stadard deviations of the different formants.

Value

A dataframe with the same numbers of rows as the formant data provided and the following columns:

formants

A column corresponding to each formant provided. These are named 'fn' where n corresponds to the formant number.

speakers

A column indicated which speaker produced each vowel.

vowels

A column indicating which vowel is represented in each row.

Author(s)

Santiago Barreda <sbarreda@ucdavis.edu>

References

Lobanov, B. M. (1971). Classification of Russian vowels spoken by different listeners. Journal of the Acoustical Society of America 49:606-08.

Nearey, T. M. (1978). Phonetic Feature Systems for Vowels. PhD thesis, Indiana University Linguistics Club.

Watt, D. and Fabricius, A. (2002). Evaluation of a technique for improving the mapping of multiple speakers' vowel spaces in the F1 ~ F2 plane. In D. Nelson, Leeds Working Papers in Linguistics and Phonetics 9:159-73.

Examples

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## normalize all Peterson & Barney (1952) vowels using each method.
data (pb52)

neareyE = normalize (pb52[,7:9], pb52$speaker, pb52$vowel,
method = 'neareyE')
neareyI = normalize (pb52[,7:9], pb52$speaker, pb52$vowel,
method = 'neareyI')
lobanov = normalize (pb52[,7:9], pb52$speaker, pb52$vowel,
method = 'lobanov')
wandf = normalize (pb52[,7:9], pb52$speaker, pb52$vowel,
method = 'wandf', corners =  c('i','A'))

## compare normalization methods using vowelplot().
par (mfrow = c(2,2), mar = c(4,4,3,1))
vowelplot (neareyE[,1], neareyE[,2], neareyE$vowel, alternateAxes = TRUE, 
  pointType = 16, main = 'neareyE', ellipses = TRUE)
vowelplot (neareyI[,1], neareyI[,2], neareyI$vowel, alternateAxes = TRUE, 
  pointType = 16, main = 'neareyI', ellipses = TRUE)
vowelplot (lobanov[,1], lobanov[,2], lobanov$vowel, alternateAxes = TRUE, 
  pointType = 16, main = 'lobanov', ellipses = TRUE)
vowelplot (wandf[,1], wandf[,2], wandf$vowel, alternateAxes = TRUE, 
  pointType = 16, main = 'wandf', ellipses = TRUE)

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