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Generic Formant DCT Normalization Procedure

Source: R/dct_norm.R
norm_dct_generic.Rd

Generic Formant DCT Normalization Procedure

Usage

norm_dct_generic(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .param_col = NULL,
  .L = 0,
  .S = 1/sqrt(2),
  .by_formant = FALSE,
  .by_token = FALSE,
  .names = "{.formant}_n",
  .silent = FALSE,
  .drop_orig = FALSE,
  .call = caller_env()
)

Arguments

.data

A data frame of formant DCT coefficients

...

<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.

.L

An expression defining the location parameter. See Details for more information.

.S

An expression defining the scale parameter. See Details for more information.

.by_formant

Whether or not the normalization method is formant intrinsic.

.by_token

Whether or not the normalization method is token intrinsic

.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.

.drop_orig

Should the originally targeted columns be dropped.

.call

Used for internal purposes.

Value

A data frame of normalized DCT coefficients.

Details

The following norm_dct_* procedures were built on top of norm_dct_generic().

Normalizing DCT Coefficients

This will normalize vowel formant data that has already had the Discrete Cosine Transform applied (see dct) with the following procedure:

  1. Location .L and Scale .S expressions will be used to summarize the zeroth DCT coefficients.

  2. These location and scale will be used to normalize the DCT coefficients.

Location and Scale expressions

norm_dct_generic normalizes DCT coefficients directly. If \(F_k\) is the kth 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_dct_generic itself, to allow greater parallelism with how norm_generic works.

Note: If you want to scale values by a constant in the normalization, you'll need to divide the constant by sqrt(2).

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

DCT normalization requires identifying individual tokens, 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.

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_dcts <- track_subset |>
  reframe_with_dct(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .order = 3
  )

track_norm <- track_dcts |>
  norm_dct_generic(
    F1:F3,
    .token_id_col = id,
    .by = speaker,
    .by_formant = TRUE,
    .L = median(.formant, na.rm = TRUE),
    .S = mad(.formant, na.rm = TRUE),
    .param_col = .param,
    .drop_orig = TRUE,
    .names = "{.formant}_mad"
  )
#> Normalization info
#> • normalized with `tidynorm::norm_dct_generic()`
#> • normalized `F1`, `F2`, and `F3`
#> • normalized values in `F1_mad`, `F2_mad`, and `F3_mad`
#> • token id column: `id`
#> • DCT parameter column: `.param`
#> • grouped by `speaker`
#> • within formant: TRUE
#> • (.formant - median(.formant, na.rm = TRUE))/mad(.formant, na.rm = TRUE)
#> 

head(track_norm)
#> # A tibble: 6 × 10
#>   speaker    id vowel plt_vclass word  .param    .n  F1_mad  F2_mad  F3_mad
#>   <chr>   <dbl> <chr> <chr>      <chr>  <dbl> <int>   <dbl>   <dbl>   <dbl>
#> 1 s01         0 EY    eyF        OKAY       0    10  0.177   0.811  -0.0952
#> 2 s01         0 EY    eyF        OKAY       1    10 -0.0837 -0.304  -0.148 
#> 3 s01         0 EY    eyF        OKAY       2    10  0.381   0.0821  0.0822
#> 4 s01         1 AH    uh         UM         0    10  0.345  -0.121   0.820 
#> 5 s01         1 AH    uh         UM         1    10  0.136   0.207  -0.255 
#> 6 s01         1 AH    uh         UM         2    10  0.0306 -0.0174 -0.0843

full_tracks <- track_norm |>
  summarise(
    .by = c(speaker, vowel, .param),
    across(
      F1_mad:F3_mad,
      mean
    )
  ) |>
  reframe_with_idct(
    F1_mad:F3_mad,
    .by = c(speaker, vowel),
    .param_col = .param
  )

head(full_tracks)
#> # A tibble: 6 × 6
#>   speaker vowel .time F1_mad F2_mad F3_mad
#>   <chr>   <chr> <int>  <dbl>  <dbl>  <dbl>
#> 1 s01     EY        1 -0.528   1.13  0.506
#> 2 s01     EY        2 -0.532   1.15  0.515
#> 3 s01     EY        3 -0.541   1.18  0.531
#> 4 s01     EY        4 -0.554   1.23  0.553
#> 5 s01     EY        5 -0.573   1.30  0.578
#> 6 s01     EY        6 -0.596   1.37  0.604

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