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Normalizing Formant Tracks

Source: vignettes/normalizing_formant_tracks.qmd

Tidynorm normalizes vowel formant tracks by

  1. Converting them to Discrete Cosine Transform coefficients.
  2. Directly normalizing the DCT coefficients.
  3. Applying the inverse DCT.

Token IDs

In order to do this successfully, each vowel token needs to be uniquely identifiable with a token id, or a token id in combination with other columns. For example, in tidynorm::speaker_tracks the column speaker combined with the column id identifies each unique vowel formant track.

speaker_tracks
#> # A tibble: 19,500 × 9
#>    speaker    id vowel plt_vclass word      t    F1    F2    F3
#>    <chr>   <dbl> <chr> <chr>      <chr> <dbl> <dbl> <dbl> <dbl>
#>  1 s01         0 EY    eyF        OKAY   32.4  754. 2145. 2913.
#>  2 s01         0 EY    eyF        OKAY   32.4  719. 2155. 2913.
#>  3 s01         0 EY    eyF        OKAY   32.4  752. 2115. 2914.
#>  4 s01         0 EY    eyF        OKAY   32.4  762. 2087. 2931.
#>  5 s01         0 EY    eyF        OKAY   32.4  738. 2088. 2933.
#>  6 s01         0 EY    eyF        OKAY   32.4  697. 2123. 2936.
#>  7 s01         0 EY    eyF        OKAY   32.4  640. 2143. 2928.
#>  8 s01         0 EY    eyF        OKAY   32.5  540. 2153. 2936.
#>  9 s01         0 EY    eyF        OKAY   32.5  441. 2164. 2936.
#> 10 s01         0 EY    eyF        OKAY   32.5  497. 2201. 2945.
#> # ℹ 19,490 more rows

For most normalization procedures, we’ll want to group the data by the speaker column anyway, and in those cases it’s sufficient to pass id to the .token_id_col argument of norm_track_* functions.

We can Lobanov normalize these speakers’ formant tracks with norm_track_lobanov().

normed_tracks <- speaker_tracks |>
  norm_track_lobanov(
    # identify the formant columns
    F1:F3,

    # provide speaker grouping
    .by = speaker,

    # provide token id
    .token_id_col = id,

    # provide an optional time column
    .time_col = t
  )
#> Normalization info
#> • normalized with `tidynorm::norm_track_lobanov()`
#> • normalized `F1`, `F2`, and `F3`
#> • normalized values in `F1_z`, `F2_z`, and `F3_z`
#> • token id column: `id`
#> • time column: `t`
#> • grouped by `speaker`
#> • within formant: TRUE
#> • (.formant - mean(.formant, na.rm = T))/sd(.formant, na.rm = T)
normed_tracks |>
  ggplot(
    aes(F2_z, F1_z)
  ) +
  geom_path(
    aes(
      group = interaction(speaker, id)
    ),
    alpha = 0.3
  ) +
  scale_y_reverse() +
  scale_x_reverse() +
  facet_wrap(~speaker) +
  coord_cartesian(
    xlim = c(3.5, -3.5),
    ylim = c(3.5, -3.5)
  ) +
  theme(
    aspect.ratio = 1
  )