Watt and Fabricius Track normalization

Usage

norm_track_wattfab(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .time_col = NULL,
  .order = 5,
  .return_dct = FALSE,
  .drop_orig = 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.
.token_id_col: <data-masking> A column that identifies token ids.
.by: <tidy-select> A selection of columns to group by. Typically a column of speaker IDs.
.time_col: <data-masking> A time column. (optional)
.order: The number of DCT parameters to use.
.return_dct: Whether or not the normalized DCT coefficients themselves should be returned.
.drop_orig: Should the originally targeted columns be dropped.
.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 frame of Watt & Fabricius normalized formant tracks.

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)
library(dplyr)
ggplot2_inst <- require(ggplot2)

track_subset <- speaker_tracks |>
  filter(
    .by = c(speaker, id),
    if_all(
      F1:F3,
      .fns =\(x) mean(is.finite(x)) > 0.9
    ),
    row_number() %% 2 == 1
  )

track_norm <- track_subset |>
  norm_track_wattfab(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE
  )

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



# returning the DCT coefficients
track_norm_dct <- track_subset |>
  norm_track_wattfab(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE,
    .return_dct = TRUE,
    .names = "{.formant}_wf"
  )

track_norm_means <- track_norm_dct |>
  summarise(
    .by = c(speaker, vowel, .param),
    across(
      ends_with("_wf"),
      mean
    )
  ) |>
  reframe_with_idct(
    ends_with("_wf"),
    .by = speaker,
    .token_id_col = vowel,
    .param_col = .param
  )


if(ggplot2_inst){
  track_norm_means|>
    ggplot(
      aes(F2_wf, F1_wf, color = speaker)
    )+
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    )+
    scale_x_reverse()+
    scale_y_reverse()+
    scale_color_brewer(palette = "Dark2")+
    coord_fixed()
}