Nearey DCT Normalization

Usage

norm_dct_nearey(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .by_formant = FALSE,
  .param_col = NULL,
  .drop_orig = FALSE,
  .names = "{.formant}_lm",
  .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.
.by_formant: Whether or not the normalization method is formant intrinsic.
.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 Nearey normalized DCT coefficients

Details

Important: This function assumes that the DCT coefficients were estimated over log-transformed formant values.

When formant extrinsic: $$ \hat{F}_{ij} = \log(F_{ij}) - L $$ $$ L = \frac{1}{MN}\sum_{i=1}^M\sum_{j=1}^N \log(F_{ij}) $$

When formant intrinsic: $$ \hat{F}_{ij} = \log(F_{ij}) - L_{i} $$

$$ L_i = \frac{1}{N}\sum_{j=1}^{N}\log(F_{ij}) $$

Where

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

References

Nearey, T. M. (1978). Phonetic Feature Systems for Vowels [Ph.D.]. University of Alberta.

Examples

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

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

# Normalize DCT coefficients
speaker_dct_norm <- speaker_dct |>
  norm_dct_nearey(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .param_col = .param
  )
#> Normalization info
#> • normalized with `tidynorm::norm_dct_nearey()`
#> • normalized `F1`, `F2`, and `F3`
#> • normalized values in `F1_lm`, `F2_lm`, and `F3_lm`
#> • token id column: `id`
#> • DCT parameter column: `.param`
#> • grouped by `speaker`
#> • within formant: FALSE
#> • (.formant - mean(.formant, na.rm = T))/(1/sqrt(2))
#> 

# Apply average and apply inverse dct
# to plot tracks
track_norm_means <- speaker_dct_norm |>
  summarise(
    .by = c(speaker, vowel, .param),
    across(
      ends_with("_lm"),
      mean
    )
  ) |>
  reframe_with_idct(
    ends_with("_lm"),
    .by = speaker,
    .token_id_col = vowel,
    .param_col = .param
  )


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_lm, F1_lm, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}