Watt and Fabricius DCT normalization

Watt and Fabricius DCT normalization

Usage

norm_dct_wattfab(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .param_col = NULL,
  .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.

.param_col

A column identifying the DCT parameter number.

.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 DCT coefficients.

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)

speaker_dct <- speaker_tracks |>
  reframe_with_dct(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t
  )

# Normalize DCT coefficients
speaker_dct_norm <- speaker_dct |>
  norm_dct_wattfab(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .param_col = .param
  )
#> Normalization info
#> • normalized with `tidynorm::norm_dct_wattfab()`
#> • normalized `F1`, `F2`, and `F3`
#> • normalized values in `F1_wf`, `F2_wf`, and `F3_wf`
#> • token id column: `id`
#> • DCT parameter column: `.param`
#> • grouped by `speaker`
#> • within formant: TRUE
#> • (.formant - 0)/mean(.formant, na.rm = T)
#> 

# Apply average and apply inverse dct
# to plot tracks
track_norm_means <- speaker_dct_norm |>
  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()
}