---
title: "Normalizing Formant Tracks"
fig-width: 5
fig-height: 3
out-width: 80%
knitr:
  opts_chunk:
    crop: !expr 'rlang::is_installed(c("magick"))'
    collapse: true
    comment: '#>'
format:
  html:
    toc: true
    html-math-method: mathjax
    embed-resources: true
    theme: none
    minimal: true
vignette: >
  %\VignetteIndexEntry{Normalizing Formant Tracks}
  %\VignetteEngine{quarto::html}
  %\VignetteEncoding{UTF-8}
---

```{r}
#| eval: !expr 'rlang::is_installed("magick")'
#| echo: false
knitr::knit_hooks$set(crop = knitr::hook_pdfcrop)
```

```{r}
#| label: setup
library(tidynorm)
```

```{r}
#| eval: !expr 'rlang::is_installed(c("ggplot2"))'
library(ggplot2)
```

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.

```{r}
speaker_tracks
```

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()`.

```{r}
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
  )
```

```{r}
#| fig-align: center
#| out-width: 80%
#| eval: !expr 'rlang::is_installed(c("ggplot2"))'
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
  )
```