Generic Formant Track Normalization Procedure — norm_track

Normalize formant tracks using Discrete Cosine Transform normalization

Usage

norm_track_generic(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .by_formant = FALSE,
  .by_token = FALSE,
  .time_col = NULL,
  .L = 0,
  .S = 1/sqrt(2),
  .pre_trans = function(x) x,
  .post_trans = function(x) x,
  .order = 5,
  .return_dct = FALSE,
  .drop_orig = FALSE,
  .names = "{.formant}_n",
  .silent = FALSE,
  .call = caller_env()
)

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.
.by_token: Whether or not the normalization method is token intrinsic
.time_col: <data-masking> A time column. (optional)
.L: An expression defining the location parameter. See Details for more information.
.S: An expression defining the scale parameter. See Details for more information.
.pre_trans: A function to apply to formant values before normalization.
.post_trans: A function to apply to formant values after normalization.
.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.
.call: Used for internal purposes.

Value

A data frame of normalized formant tracks.

Details

This will normalize vowel formant tracks in the following steps:

Any .pre_trans transformations will be applied to the formant data.
The Discrete Cosine Transform will be applied to the formant data.
Location .L and Scale .S expressions will be used to summarize the zero^th DCT coefficients.
These location and scale will be used to normalize the DCT coefficients.
If .return_dct = TRUE, these normalized DCT coefficients will be returned. Otherwise, the Inverse Discrete Cosine Transform will be applied to the normalized DCT coefficients.
Any .post_trans transformations will be applied.

Location and Scale expressions

All normalization procedures built on norm_track_generic work by normalizing DCT coefficients directly. If $F_k$ is the k^th DCT coefficient the normalization procedure is

$$ \hat{F}_k = \frac{F_k - L'}{\sqrt{2}S} $$ $$ L' = \begin{cases} L & \text{for }k=0\\ 0 & \text{for }k>0 \end{cases} $$

Rather than requiring users to remember to multiply expressions for $S$ by $\sqrt{2}$, this is done by norm_track_generic itself, to allow greater parallelism with how norm_generic works.

The expressions for calculating $L$ and $S$ can be passed to .L and .S, respectively. Available values for these expressions are

.formant: The original formant value
.formant_num: The number of the formant. (e.g. 1 for F1, 2 for F2 etc)

Along with any data columns from your original data.

Identifying tokens

The DCT only works on a by-token basis, so there must be a column that uniquely identifies (or, in combination with a .by grouping, uniquely identifies) each individual token. This column should be passed to .token_id_col.

Order

The number of DCT coefficients used is defined by .order. The default value is 5. Larger numbers will lead to less smoothing, and smaller numbers will lead to more smoothing.

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_generic(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .by_formant = TRUE,
    .L = median(.formant, na.rm = TRUE),
    .S = mad(.formant, na.rm = TRUE),
    .time_col = t,
    .drop_orig = TRUE,
    .names = "{.formant}_mad"
  )

if(ggplot2_inst){
  track_norm |>
    ggplot(
      aes(F2_mad, F1_mad, 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_generic(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .by_formant = TRUE,
    .L = median(.formant, na.rm = TRUE),
    .S = mad(.formant, na.rm = TRUE),
    .time_col = t,
    .drop_orig = TRUE,
    .return_dct = TRUE,
    .names = "{.formant}_mad"
  )

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


if(ggplot2_inst){
  track_norm_means|>
    ggplot(
      aes(F2_mad, F1_mad, color = speaker)
    )+
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    )+
    scale_x_reverse()+
    scale_y_reverse()+
    scale_color_brewer(palette = "Dark2")+
    coord_fixed()
}