Watt & Fabricius Normalize

Usage

norm_wattfab(
  .data,
  ...,
  .by = NULL,
  .by_formant = TRUE,
  .drop_orig = FALSE,
  .keep_params = FALSE,
  .names = "{.formant}_wf",
  .silent = FALSE
)

Arguments

.data: A data frame containing vowel formant data
...: <tidy-select> One or more unquoted expressions separated by commas. These should target the vowel formant data columns.
.by: <tidy-select> A selection of columns to group by. Typically a column of speaker IDs.
.by_formant: Ignored by this procedure
.drop_orig: Whether or not to drop the original formant data columns.
.keep_params: Whether or not to keep the Location (*_.L) and Scale (*_.S) normalization parameters
.names: A glue::glue() expression for naming the normalized data columns. The "{.formant}" portion corresponds to the name of the original formant columns.
.silent: Whether or not the informational message should be printed.

Value

A data fame of Watt & Fabricius normalized formant values.

Details

This is a modified version of the Watt & Fabricius Method. The original method identified point vowels over which F1 and F2 centroids were calculated. The procedure here just identifies centroids by taking the mean of all formant values.

$$ \hat{F}_{ij} = \frac{F_{ij}}{S_i} $$

$$ S_i = \frac{1}{N}\sum_{j=1}^N F_{ij} $$

Where

$\hat{F}$ is the normalized formant
$i$ is the formant number
$j$ is the token number

References

Watt, D., & Fabricius, A. (2002). Evaluation of a technique for improving the mapping of multiple speakers’ vowel spaces in the F1 ~ F2 plane. Leeds Working Papers in Linguistics and Phonetics, 9, 159–173.

Examples

library(tidynorm)
ggplot2_inst <- require(ggplot2)

speaker_data_wattfab <- speaker_data |>
  norm_wattfab(
    F1:F3,
    .by = speaker,
    .names = "{.formant}_wf"
  )
#> Normalization info
#> • normalized `F1`, `F2`, and `F3`
#> • normalized values in `F1_wf`, `F2_wf`, and `F3_wf`
#> • grouped by `speaker`
#> • formant intrinsic
#> 

if(ggplot2_inst){
  ggplot(
    speaker_data_wattfab,
    aes(
      F2_wf,
      F1_wf,
      color = speaker
    )
  )+
    stat_density_2d(
      bins = 4
    )+
    scale_color_brewer(
      palette = "Dark2"
    )+
    scale_x_reverse()+
    scale_y_reverse()+
    coord_fixed()
}