tidynorm: Tools for Tidy Vowel Normalization

Description

An implementation of tidy speaker vowel normalization. This includes generic functions for defining new normalization methods for points, formant tracks, and Discrete Cosine Transform coefficients, as well as convenience functions implementing established normalization methods. References for the implemented methods are: Johnson, Keith (2020) doi:10.5334/labphon.196 Lobanov, Boris (1971) doi:10.1121/1.1912396 Nearey, Terrance M. (1978) https://sites.ualberta.ca/~tnearey/Nearey1978_compressed.pdf Syrdal, Ann K., and Gopal, H. S. (1986) doi:10.1121/1.393381 Watt, Dominic, and Fabricius, Anne (2002) https://www.latl.leeds.ac.uk/article/evaluation-of-a-technique-for-improving-the-mapping-of-multiple-speakers-vowel-spaces-in-the-f1-f2-plane/.

Author(s)

Maintainer: Josef Fruehwald JoFrhwld@gmail.com [copyright holder]

See Also

Useful links:

• https://jofrhwld.github.io/tidynorm/

• https://github.com/JoFrhwld/tidynorm

• Report bugs at https://github.com/JoFrhwld/tidynorm/issues

Bark to Hz

Description

Converts bark to Hz

Usage

bark_to_hz(bark)

Arguments

Details

\hat{b} = \begin{cases} \frac{b - 0.3}{0.85} & \text{if} ~ b < 2\\ \frac{b + 4.422}{1.22} & \text{if} ~ b > 20.1\\ b & \text{otherwise} \end{cases}

hz = 1960\frac{\hat{b} + 0.53}{26.28 - \hat{b}}

Value

A vector of Hz scaled values

References

Traunmüller, H. (1990). Analytical expressions for the tonotopic sensory scale. The Journal of the Acoustical Society of America, 88(1), 97–100. doi:10.1121/1.399849

Examples

bark <- seq(1.5, 13, length = 100)
hz <- bark_to_hz(bark)
plot(bark, hz)

Check Normalization Procedures

Description

check_norm() will generate a message with information about which normalization procedures have been applied to the data.

Usage

check_norm(.data)

Arguments

Value

This only prints an info message.

Examples

speaker_norm <- speaker_data |>
  norm_nearey(
    F1:F3,
    .by = speaker,
    .silent = TRUE
  )

check_norm(speaker_norm)

Discrete Cosine Transform

Description

Discrete Cosine Transform

Usage

dct(x)

## S3 method for class 'numeric'
dct(x)

## S3 method for class 'matrix'
dct(x)

Arguments

Details

The DCT definitions here are based on the python scipy.fft.dct definitions. Specifically this use:

# python code
scipy.fft.dct(x, norm = "forward", orthogonalize = True)

y_k = \frac{1}{zN} \sum_{j=0}^{N-1}x_j\cos\left(\frac{\pi k(2j+1)}{2N}\right)

z = \begin{cases} \sqrt{2}& \text{for }k=0\\ 1 & \text{for }k>0 \end{cases}

For the Inverse Discrete Cosine Transform, see idct.

Value

Returned value depends on x.

When passed a numeric vector, returns a numeric vector the same size as x with the DCT Coefficients.

When passed a matrix, returns a matrix the same size as x with the DCT Coefficients.

Examples

x <- seq(0, 1, length = 10)
y <- 5 + x + (2 * (x^2)) + (-2 * (x^4))

dct_coefs <- dct(y)

DCT Basis

Description

The Discrete Cosine Transform basis functions

Usage

dct_basis(n, k)

Arguments

Details

This function will generate the DCT basis functions.

Value

A n\times k matrix

Examples

basis <- dct_basis(100, 5)
matplot(basis, type = "l", lty = 1)

Hz to Bark

Description

Converts Hz to Bark

Usage

hz_to_bark(hz)

Arguments

Details

\hat{b} = \frac{26.81 hz}{1960 + hz} - 0.53

b = \begin{cases} \hat{b} + 0.15(2-\hat{b}) & \text{if}~\hat{b} < 2\\ \hat{b} + 0.22(\hat{b} - 20.1) & \text{if}~\hat{b} > 20.1\\ \hat{b} & \text{otherwise} \end{cases}

Value

A vector of bark scaled values

References

Traunmüller, H. (1990). Analytical expressions for the tonotopic sensory scale. The Journal of the Acoustical Society of America, 88(1), 97–100. doi:10.1121/1.399849

Examples

hz <- seq(150, 2000, length = 100)
bark <- hz_to_bark(hz)
plot(hz, bark)

Hz to Mel

Description

Convert Hz to Mel

Usage

hz_to_mel(hz, htk = FALSE)

Arguments

Details

This is a direct re-implementation of the hz_to_mel function from the librosa library.

The default method is to use the method due to Slaney (1998), which is linear below 1000Hz, and logarithmic above.

If htk=TRUE, the method from HTK, due to O'Shaughnessy (1987) is used.

Value

A numeric vector of Mel values

References

McFee, B., C. Raffel, D. Liang, D. PW Ellis, M. McVicar, E. Battenberg, and O. Nieto. librosa: Audio and music signal analysis in python. In Proceedings of the 14th python in science conference, pp. 18-25.

O'Shaughnessy, D (1987). Speech communication: human and machine. Addison-Wesley. p. 150. ISBN 978-0-201-16520-3.

Slaney, M. (1998) Auditory Toolbox: A MATLAB Toolbox for Auditory Modeling Work. Technical Report, version 2, Interval Research Corporation.

Examples

hz_to_mel(c(500, 1000, 2000, 3000))

Inverse Discrete Cosine Transform

Description

The Inverse DCT

Usage

idct(y, n)

## S3 method for class 'numeric'
idct(y, n = length(y))

## S3 method for class 'matrix'
idct(y, n = nrow(y))

Arguments

Details

Applies the Inverse DCT (see dct for more details).

x_j = \sqrt{2}y_0 + 2\sum_{k=1}^{N-1} y_k \cos\left(\frac{\pi k(2j+1)}{2J}\right)

Value

The returned value depends on the values in y.

When passed a numeric vector, returns numeric vector of length n.

When passed a matrix, returns a matrix with n rows and the same number of columns as y.

Examples

x <- seq(0, 1, length = 10)
y <- 5 + x + (2 * (x^2)) + (-2 * (x^4))

dct_coefs <- dct(y)
recovered_y <- idct(dct_coefs)

plot(y, recovered_y)

Inverse Discrete Cosine Transform Acceleration

Description

The second derivative of the Inverse DCT

Usage

idct_accel(y, n = length(y))

Arguments

Details

Returns the second derivative (acceleration) of the Inverse DCT (see dct for more details).

\frac{\delta^2 x_j}{\delta j^2} = -2\left(\frac{\pi k}{J}\right)^2\sum_{k=1}^{N-1} y_k \cos\left(\frac{\pi k(2j+1)}{2J}\right)

Value

A vector with the second derivative of the inverse DCT

Examples

x <- seq(0, 1, length = 10)
y <- 5 + x + (2 * (x^2)) + (-2 * (x^4))

dct_coefs <- dct(y)
y_accel <- idct_accel(dct_coefs)

plot(y)
plot(y_accel)

Inverse Discrete Cosine Transform Rate

Description

The first derivative of the Inverse DCT

Usage

idct_rate(y, n = length(y))

Arguments

Details

Returns the first derivative (rate of change) of the Inverse DCT (see dct for more details).

\frac{\delta x_j}{\delta j} = -2\frac{\pi k}{J}\sum_{k=1}^{N-1} y_k \sin\left(\frac{\pi k(2j+1)}{2J}\right)

Value

A vector with the first derivative of the inverse DCT

Examples

x <- seq(0, 1, length = 10)
y <- 5 + x + (2 * (x^2)) + (-2 * (x^4))

dct_coefs <- dct(y)
y_rate <- idct_rate(dct_coefs)

plot(y)
plot(y_rate)

Mel to Hz

Description

Convert Mel to Hz

Usage

mel_to_hz(mel, htk = FALSE)

Arguments

Details

This is a direct re-implementation of the hz_to_mel function from the librosa library.

The default method is to use the method due to Slaney (1998), which is linear below 1000Hz, and logarithmic above.

If htk=TRUE, the method from HTK, due to O'Shaughnessy (1987) is used.

Value

A numeric vector of Hz values

References

McFee, B., C. Raffel, D. Liang, D. PW Ellis, M. McVicar, E. Battenberg, and O. Nieto. librosa: Audio and music signal analysis in python. In Proceedings of the 14th python in science conference, pp. 18-25.

O'Shaughnessy, D (1987). Speech communication: human and machine. Addison-Wesley. p. 150. ISBN 978-0-201-16520-3.

Slaney, M. (1998) Auditory Toolbox: A MATLAB Toolbox for Auditory Modeling Work. Technical Report, version 2, Interval Research Corporation.

Examples

mel_to_hz(c(7.5, 15, 25, 31))

Bark Difference Normalize

Description

Bark Difference Normalize

Usage

norm_barkz(
  .data,
  ...,
  .by = NULL,
  .drop_orig = FALSE,
  .keep_params = FALSE,
  .names = "{.formant}_bz",
  .silent = FALSE
)

Arguments

Details

This is a within-token normalization technique. First all formants are converted to Bark (see hz_to_bark), then, within each token, F3 is subtracted from F1 and F2.

\hat{F}_{ij} = F_{ij} - L_j

L_j = F_{3j}

Value

A data frame of Bark Difference normalized formant values

References

Syrdal, A. K., & Gopal, H. S. (1986). A perceptual model of vowel recognition based on the auditory representation of American English vowels. The Journal of the Acoustical Society of America, 79(4), 1086–1100. doi:10.1121/1.393381

Examples

library(tidynorm)
ggplot2_inst <- require(ggplot2)

speaker_data_barkz <- speaker_data |>
  norm_barkz(
    F1:F3,
    .by = speaker,
    .names = "{.formant}_bz"
  )

if (ggplot2_inst) {
  ggplot(
    speaker_data_barkz,
    aes(
      F2_bz,
      F1_bz,
      color = speaker
    )
  ) +
    stat_density_2d(
      bins = 4
    ) +
    scale_color_brewer(
      palette = "Dark2"
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    coord_fixed()
}

Bark Difference DCT Normalization

Description

Bark Difference DCT Normalization

Usage

norm_dct_barkz(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .param_col = NULL,
  .drop_orig = FALSE,
  .names = "{.formant}_bz",
  .silent = FALSE
)

Arguments

Details

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

This is a within-token normalization technique. First all formants are converted to Bark (see hz_to_bark), then, within each token, F3 is subtracted from F1 and F2.

\hat{F}_{ij} = F_{ij} - L_j

L_j = F_{3j}

Value

A data frame of normalized DCT parameters.

A data frame of Back Difference normalized dct coefficients.

References

Syrdal, A. K., & Gopal, H. S. (1986). A perceptual model of vowel recognition based on the auditory representation of American English vowels. The Journal of the Acoustical Society of America, 79(4), 1086–1100. doi:10.1121/1.393381

Examples

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

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

# Normalize DCT coefficients
speaker_dct_norm <- speaker_dct |>
  norm_dct_barkz(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .param_col = .param
  )

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


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_bz, F1_bz, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}

Delta F DCT Normalization

Description

Delta F DCT Normalization

Usage

norm_dct_deltaF(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .param_col = NULL,
  .drop_orig = FALSE,
  .names = "{.formant}_df",
  .silent = FALSE
)

Arguments

Details

\hat{F}_{ij} = \frac{F_{ij}}{S}

S = \frac{1}{MN}\sum_{i=1}^M\sum_{j=1}^N \frac{F_{ij}}{i-0.5}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data frame of Delta F normalized DCT coefficients.

References

Johnson, K. (2020). The \DeltaF method of vocal tract length normalization for vowels. Laboratory Phonology: Journal of the Association for Laboratory Phonology, 11(1), Article 1. doi:10.5334/labphon.196

Examples

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

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

# Normalize DCT coefficients
speaker_dct_norm <- speaker_dct |>
  norm_dct_deltaF(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .param_col = .param
  )

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


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_df, F1_df, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}

Generic Formant DCT Normalization Procedure

Description

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

Details

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

• norm_dct_lobanov

• norm_dct_nearey

• norm_dct_deltaF

• norm_dct_wattfab

• norm_dct_barkz

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 zero^th 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 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_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.

Value

A data frame of normalized DCT coefficients.

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"
  )

head(track_norm)

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)

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()
}

Lobanov DCT Normalization

Description

Lobanov DCT Normalization

Usage

norm_dct_lobanov(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .param_col = NULL,
  .names = "{.formant}_z",
  .silent = FALSE,
  .drop_orig = FALSE
)

Arguments

Details

\hat{F}_{ij} = \frac{F_{ij} - L_i}{S_i}

L_i = \frac{1}{N}\sum_{j=1}^{N}F_{ij}

S_i = \sqrt{\frac{\sum(F_{ij}-L_i)^2}{N-1}}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data frame of Lobanov normalized DCT Coefficients.

References

Lobanov, B. (1971). Classification of Russian vowels spoken by different listeners. Journal of the Acoustical Society of America, 49, 606–608.

Examples

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

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

# Normalize DCT coefficients
speaker_dct_norm <- speaker_dct |>
  norm_dct_lobanov(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .param_col = .param
  )

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


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_z, F1_z, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}

Nearey DCT Normalization

Description

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

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

Value

A data frame of Nearey normalized DCT coefficients

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
  )

# 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()
}

Watt and Fabricius DCT normalization

Description

Watt and Fabricius DCT normalization

Usage

norm_dct_wattfab(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .param_col = NULL,
  .drop_orig = FALSE,
  .names = "{.formant}_wf",
  .silent = FALSE
)

Arguments

Details

This is a modified version of the Watt & Fabricius Method. The original method identified point vowels over which F1 and F2 centroids were calculated. The procedure here just identifies centroids by taking the mean of all formant values.

\hat{F}_{ij} = \frac{F_{ij}}{S_i}

S_i = \frac{1}{N}\sum_{j=1}^N F_{ij}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data frame of Watt & Fabricius normalized DCT coefficients.

References

Watt, D., & Fabricius, A. (2002). Evaluation of a technique for improving the mapping of multiple speakers’ vowel spaces in the F1 ~ F2 plane. Leeds Working Papers in Linguistics and Phonetics, 9, 159–173.

Examples

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

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

# Normalize DCT coefficients
speaker_dct_norm <- speaker_dct |>
  norm_dct_wattfab(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .param_col = .param
  )

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


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_wf, F1_wf, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}

Delta F Normalize

Description

Delta F Normalize

Usage

norm_deltaF(
  .data,
  ...,
  .by = NULL,
  .by_formant = FALSE,
  .drop_orig = FALSE,
  .keep_params = FALSE,
  .names = "{.formant}_df",
  .silent = FALSE
)

Arguments

Details

\hat{F}_{ij} = \frac{F_{ij}}{S}

S = \frac{1}{MN}\sum_{i=1}^M\sum_{j=1}^N \frac{F_{ij}}{i-0.5}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data frame of Delta F normalized formant values.

References

Johnson, K. (2020). The \DeltaF method of vocal tract length normalization for vowels. Laboratory Phonology: Journal of the Association for Laboratory Phonology, 11(1), Article 1. doi:10.5334/labphon.196

Examples

library(tidynorm)
ggplot2_inst <- require(ggplot2)

speaker_data_deltaF <- speaker_data |>
  norm_deltaF(
    F1:F3,
    .by = speaker,
    .names = "{.formant}_df"
  )

if (ggplot2_inst) {
  ggplot(
    speaker_data_deltaF,
    aes(
      F2_df,
      F1_df,
      color = speaker
    )
  ) +
    stat_density_2d(
      bins = 4
    ) +
    scale_color_brewer(
      palette = "Dark2"
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    coord_fixed()
}

Generic Normalization Procedure

Description

This is a generic normalization procedure with which you can create your own normalization method.

Usage

norm_generic(
  .data,
  ...,
  .by = NULL,
  .by_formant = FALSE,
  .by_token = FALSE,
  .L = 0,
  .S = 1,
  .pre_trans = function(x) x,
  .post_trans = function(x) x,
  .drop_orig = FALSE,
  .keep_params = FALSE,
  .names = "{.formant}_n",
  .silent = FALSE,
  .call = caller_env()
)

Arguments

Details

The following ⁠norm_*⁠ procedures are built on top of norm_generic().

• norm_lobanov

• norm_nearey

• norm_deltaF

• norm_wattfab

• norm_barkz

Location and Scale expressions

All normalization procedures built on norm_generic produce normalized formant values (\hat{F}) by subtracting a location parameter (L) and dividing by a scale parameter (S).

\hat{F} = \frac{F-L}{S}

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.

Pre and Post normalization transforms

To apply any transformations before or after normalization, you can pass a function to .pre_trans and .post_trans.

Formant In/Extrinsic Normalization

If .by_formant is TRUE, normalization will be formant intrinsic. If .by_formant is FALSE, normalization will be formant extrinsic.

Token In/Extrinsic Normalization

If .by_token is TRUE, normalization will be token intrinsic. If .by_token is FALSE, normalization will be token extrinsic.

Value

A data frame of normalized formant values

Examples

library(tidynorm)
library(dplyr)

speaker_data |>
  norm_generic(
    F1:F3,
    .by = speaker,
    .by_formant = TRUE,
    .L = median(.formant, na.rm = TRUE),
    .S = mad(.formant, na.rm = TRUE),
    .drop_orig = TRUE,
    .names = "{.formant}_mad"
  )

Lobanov Normalize

Description

Lobanov Normalize

Usage

norm_lobanov(
  .data,
  ...,
  .by = NULL,
  .by_formant = TRUE,
  .drop_orig = FALSE,
  .keep_params = FALSE,
  .names = "{.formant}_z",
  .silent = FALSE
)

Arguments

Details

\hat{F}_{ij} = \frac{F_{ij} - L_i}{S_i}

L_i = \frac{1}{N}\sum_{j=1}^{N}F_{ij}

S_i = \sqrt{\frac{\sum(F_{ij}-L_i)^2}{N-1}}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data frame of Lobanov normalized formant values.

References

Lobanov, B. (1971). Classification of Russian vowels spoken by different listeners. Journal of the Acoustical Society of America, 49, 606–608.

Examples

library(tidynorm)
ggplot2_inst <- require(ggplot2)

speaker_data_lobanov <- speaker_data |>
  norm_lobanov(
    F1:F3,
    .by = speaker,
    .names = "{.formant}_z"
  )

if (ggplot2_inst) {
  ggplot(
    speaker_data_lobanov,
    aes(
      F2_z,
      F1_z,
      color = speaker
    )
  ) +
    stat_density_2d(
      bins = 4
    ) +
    scale_color_brewer(
      palette = "Dark2"
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    coord_fixed()
}

Nearey Normalize

Description

Nearey Normalize

Usage

norm_nearey(
  .data,
  ...,
  .by = NULL,
  .by_formant = FALSE,
  .drop_orig = FALSE,
  .keep_params = FALSE,
  .names = "{.formant}_lm",
  .silent = FALSE
)

Arguments

Details

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

Value

A data frame of Nearey normalized formant values.

References

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

Examples

library(tidynorm)
ggplot2_inst <- require(ggplot2)

speaker_data_nearey <- speaker_data |>
  norm_nearey(
    F1:F3,
    .by = speaker,
    .by_formant = FALSE,
    .names = "{.formant}_nearey"
  )

if (ggplot2_inst) {
  ggplot(
    speaker_data_nearey,
    aes(
      F2_nearey,
      F1_nearey,
      color = speaker
    )
  ) +
    stat_density_2d(
      bins = 4
    ) +
    scale_color_brewer(
      palette = "Dark2"
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    coord_fixed() +
    labs(
      title = "Formant extrinsic"
    )
}

speaker_data_nearey2 <- speaker_data |>
  norm_nearey(
    F1:F3,
    .by = speaker,
    .by_formant = TRUE,
    .names = "{.formant}_nearey"
  )

if (ggplot2_inst) {
  ggplot(
    speaker_data_nearey2,
    aes(
      F2_nearey,
      F1_nearey,
      color = speaker
    )
  ) +
    stat_density_2d(
      bins = 4
    ) +
    scale_color_brewer(
      palette = "Dark2"
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    coord_fixed() +
    labs(
      title = "Formant intrinsic"
    )
}

Bark Difference Track Normalization

Description

Bark Difference Track Normalization

Usage

norm_track_barkz(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .time_col = NULL,
  .order = 5,
  .return_dct = FALSE,
  .drop_orig = FALSE,
  .names = "{.formant}_bz",
  .silent = FALSE
)

Arguments

Details

This is a within-token normalization technique. First all formants are converted to Bark (see hz_to_bark), then, within each token, F3 is subtracted from F1 and F2.

\hat{F}_{ij} = F_{ij} - L_j

L_j = F_{3j}

Value

A data frame of either normalized formant tracks, or normalized DCT parameters.

A data frame of Bark difference normalized formant tracks.

References

Syrdal, A. K., & Gopal, H. S. (1986). A perceptual model of vowel recognition based on the auditory representation of American English vowels. The Journal of the Acoustical Society of America, 79(4), 1086–1100. doi:10.1121/1.393381

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_barkz(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE
  )

if (ggplot2_inst) {
  track_norm |>
    ggplot(
      aes(F2_bz, F1_bz, 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_barkz(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE,
    .return_dct = TRUE,
    .names = "{.formant}_bz"
  )

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


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_bz, F1_bz, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}

Delta F Track Normalization

Description

Delta F Track Normalization

Usage

norm_track_deltaF(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .time_col = NULL,
  .order = 5,
  .return_dct = FALSE,
  .drop_orig = FALSE,
  .names = "{.formant}_df",
  .silent = FALSE
)

Arguments

Details

\hat{F}_{ij} = \frac{F_{ij}}{S}

S = \frac{1}{MN}\sum_{i=1}^M\sum_{j=1}^N \frac{F_{ij}}{i-0.5}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data frame of Delta F normalized formant tracks.

References

Johnson, K. (2020). The \DeltaF method of vocal tract length normalization for vowels. Laboratory Phonology: Journal of the Association for Laboratory Phonology, 11(1), Article 1. doi:10.5334/labphon.196

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_deltaF(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE
  )

if (ggplot2_inst) {
  track_norm |>
    ggplot(
      aes(F2_df, F1_df, 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_deltaF(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE,
    .return_dct = TRUE,
    .names = "{.formant}_df"
  )

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


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_df, F1_df, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}

Generic Formant Track Normalization Procedure

Description

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

Details

The following ⁠norm_track_*⁠ procedures were built on top of norm_track_generic.

• norm_track_lobanov

• norm_track_nearey

• norm_track_deltaF

• norm_track_wattfab

• norm_track_barkz

This will normalize vowel formant tracks in the following steps:

1. Any .pre_trans transformations will be applied to the formant data.

2. The Discrete Cosine Transform will be applied to the formant data.

3. Location .L and Scale .S expressions will be used to summarize the zero^th DCT coefficients.

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

5. 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.

6. 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.

Note: If you want to scale values by a constant in the normalization, you'll need to divide the constant by sqrt(2). Post-normalization scaling (e.g. re-scaling to formant-like values) is probably best handled with a function passed to .post_trans.

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

Track 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.

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.

Value

A data frame of normalized formant tracks.

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()
}

Lobanov Track Normalization

Description

Lobanov Track Normalization

Usage

norm_track_lobanov(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .time_col = NULL,
  .order = 5,
  .return_dct = FALSE,
  .drop_orig = FALSE,
  .names = "{.formant}_z",
  .silent = FALSE
)

Arguments

Details

\hat{F}_{ij} = \frac{F_{ij} - L_i}{S_i}

L_i = \frac{1}{N}\sum_{j=1}^{N}F_{ij}

S_i = \sqrt{\frac{\sum(F_{ij}-L_i)^2}{N-1}}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data frame of Lobanov normalized formant tracks.

References

Lobanov, B. (1971). Classification of Russian vowels spoken by different listeners. Journal of the Acoustical Society of America, 49, 606–608.

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_lobanov(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE
  )

if (ggplot2_inst) {
  track_norm |>
    ggplot(
      aes(F2_z, F1_z, 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_lobanov(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .return_dct = TRUE,
    .drop_orig = TRUE,
    .names = "{.formant}_z"
  )

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


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_z, F1_z, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}

Nearey Track Normalization

Description

Nearey Track Normalization

Usage

norm_track_nearey(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .by_formant = FALSE,
  .time_col = NULL,
  .order = 5,
  .return_dct = FALSE,
  .drop_orig = FALSE,
  .names = "{.formant}_lm",
  .silent = FALSE
)

Arguments

Details

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

Value

A data frame of Nearey normalized formant tracks.

References

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

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_nearey(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .by_formant = TRUE,
    .drop_orig = TRUE
  )

if (ggplot2_inst) {
  track_norm |>
    ggplot(
      aes(F2_lm, F1_lm, 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_nearey(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .by_formant = FALSE,
    .drop_orig = TRUE,
    .return_dct = TRUE,
    .names = "{.formant}_lm"
  )

track_norm_means <- track_norm_dct |>
  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()
}

Watt and Fabricius Track normalization

Description

Watt and Fabricius Track normalization

Usage

norm_track_wattfab(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .time_col = NULL,
  .order = 5,
  .return_dct = FALSE,
  .drop_orig = FALSE,
  .names = "{.formant}_wf",
  .silent = FALSE
)

Arguments

Details

This is a modified version of the Watt & Fabricius Method. The original method identified point vowels over which F1 and F2 centroids were calculated. The procedure here just identifies centroids by taking the mean of all formant values.

\hat{F}_{ij} = \frac{F_{ij}}{S_i}

S_i = \frac{1}{N}\sum_{j=1}^N F_{ij}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data frame of Watt & Fabricius normalized formant tracks.

References

Watt, D., & Fabricius, A. (2002). Evaluation of a technique for improving the mapping of multiple speakers’ vowel spaces in the F1 ~ F2 plane. Leeds Working Papers in Linguistics and Phonetics, 9, 159–173.

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_wattfab(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE
  )

if (ggplot2_inst) {
  track_norm |>
    ggplot(
      aes(F2_wf, F1_wf, 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_wattfab(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .drop_orig = TRUE,
    .return_dct = TRUE,
    .names = "{.formant}_wf"
  )

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


if (ggplot2_inst) {
  track_norm_means |>
    ggplot(
      aes(F2_wf, F1_wf, color = speaker)
    ) +
    geom_path(
      aes(
        group = interaction(speaker, vowel)
      )
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    scale_color_brewer(palette = "Dark2") +
    coord_fixed()
}

Watt & Fabricius Normalize

Description

Watt & Fabricius Normalize

Usage

norm_wattfab(
  .data,
  ...,
  .by = NULL,
  .by_formant = TRUE,
  .drop_orig = FALSE,
  .keep_params = FALSE,
  .names = "{.formant}_wf",
  .silent = FALSE
)

Arguments

Details

This is a modified version of the Watt & Fabricius Method. The original method identified point vowels over which F1 and F2 centroids were calculated. The procedure here just identifies centroids by taking the mean of all formant values.

\hat{F}_{ij} = \frac{F_{ij}}{S_i}

S_i = \frac{1}{N}\sum_{j=1}^N F_{ij}

Where

• \hat{F} is the normalized formant

• i is the formant number

• j is the token number

Value

A data fame of Watt & Fabricius normalized formant values.

References

Watt, D., & Fabricius, A. (2002). Evaluation of a technique for improving the mapping of multiple speakers’ vowel spaces in the F1 ~ F2 plane. Leeds Working Papers in Linguistics and Phonetics, 9, 159–173.

Examples

library(tidynorm)
ggplot2_inst <- require(ggplot2)

speaker_data_wattfab <- speaker_data |>
  norm_wattfab(
    F1:F3,
    .by = speaker,
    .names = "{.formant}_wf"
  )

if (ggplot2_inst) {
  ggplot(
    speaker_data_wattfab,
    aes(
      F2_wf,
      F1_wf,
      color = speaker
    )
  ) +
    stat_density_2d(
      bins = 4
    ) +
    scale_color_brewer(
      palette = "Dark2"
    ) +
    scale_x_reverse() +
    scale_y_reverse() +
    coord_fixed()
}

Reframe with DCT

Description

Reframe data columns using the Discrete Cosine Transform

Usage

reframe_with_dct(
  .data,
  ...,
  .token_id_col = NULL,
  .by = NULL,
  .time_col = NULL,
  .order = 5
)

Arguments

Details

This function will tidily apply the Discrete Cosine Transform with forward normalization (see dct for more info) to the targeted columns.

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 to return is defined by .order. The default value is 5. Larger numbers will lead to less smoothing when the Inverse DCT is applied (see idct). Smaller numbers will lead to more smoothing.

If NA is passed to .order, all DCT parameters will be returned, which when the Inverse DCT is supplied, will completely reconstruct the original data.

Sorting by Time

An optional .time_col can also be defined to ensure that the data is correctly arranged by time.

Value

A data frame with with the targeted DCT coefficients, along with two additional columns

.param

The nth DCT coefficient number

.n

The number of original data values

Examples

library(tidynorm)
library(dplyr)

speaker_small <- filter(
  speaker_tracks,
  id == 0
)

speaker_dct <- reframe_with_dct(
  speaker_small,
  F1:F3,
  .by = speaker,
  .token_id_col = id,
  .time_col = t
)

head(
  speaker_dct
)

Reframe with DCT Smooth

Description

Apply a DCT Smooth to the targeted data

Usage

reframe_with_dct_smooth(
  .data,
  ...,
  .token_id_col,
  .by = NULL,
  .time_col = NULL,
  .order = 5,
  .rate = FALSE,
  .accel = FALSE
)

Arguments

Details

This is roughly equivalent to applying reframe_with_dct followed by reframe_with_idct. As long as the value passed to .order is less than the length of the each token's data, this will result in a smoothed version of the 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 to return is defined by .order. The default value is 5. Larger numbers will lead to less smoothing when the Inverse DCT is applied (see idct). Smaller numbers will lead to more smoothing.

If NA is passed to .order, all DCT parameters will be returned, which when the Inverse DCT is supplied, will completely reconstruct the original data.

Sorting by Time

An optional .time_col can also be defined to ensure that the data is correctly arranged by time.

Additionally, if .time_col is provided, the original time column will be included in the output

Value

A data frame where the target columns have been smoothed using the DCT, as well as the signal rate of change and acceleration, if requested.

Examples

library(tidynorm)
library(dplyr)

ggplot2_inst <- require(ggplot2)

speaker_small <- filter(
  speaker_tracks,
  id == 0
)

speaker_dct_smooth <- speaker_small |>
  reframe_with_dct_smooth(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .order = 5
  )

if (ggplot2_inst) {
  speaker_small |>
    ggplot(
      aes(
        t, F1
      )
    ) +
    geom_point() +
    facet_wrap(
      ~speaker,
      scales = "free_x",
      ncol = 1
    ) +
    labs(
      title = "Original Data"
    )
}

if (ggplot2_inst) {
  speaker_dct_smooth |>
    ggplot(
      aes(
        t, F1
      )
    ) +
    geom_point() +
    facet_wrap(
      ~speaker,
      scales = "free_x",
      ncol = 1
    ) +
    labs(
      title = "Smoothed Data"
    )
}

Reframe with IDCT

Description

Reframe data columns using the Inverse Discrete Cosine Transform

Usage

reframe_with_idct(
  .data,
  ...,
  .token_id_col = NULL,
  .by = NULL,
  .param_col = NULL,
  .n = 20,
  .rate = FALSE,
  .accel = FALSE
)

Arguments

Details

This will apply the Inverse Discrete Cosine Transform to the targeted columns. See idct.

Identifying tokens

The IDCT 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.

Size of the output

The output of the IDCT can be arbitrarily long as defined by the .n argument. .n can either be an integer, or an unqoted data column.

The Parameter Column

The order of the DCT parameters is crucially important. The optional .param_col will ensure the data is properly arranged.

Value

A data frame with the IDCT of the targeted columns along with an additional .time column.

.time

A column from 1 to .n by token

Examples

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

speaker_small <- filter(
  speaker_tracks,
  id == 0
)

speaker_dct <- speaker_small |>
  reframe_with_dct(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .time_col = t,
    .order = 5
  )

speaker_idct <- speaker_dct |>
  reframe_with_idct(
    F1:F3,
    .by = speaker,
    .token_id_col = id,
    .param_col = .param,
    .n = 20
  )

if (ggplot2_inst) {
  speaker_small |>
    mutate(
      .by = c(speaker, id),
      time_index = row_number()
    ) |>
    ggplot(
      aes(
        time_index, F1
      )
    ) +
    geom_point() +
    labs(
      title = "Original Data"
    )
}

if (ggplot2_inst) {
  speaker_idct |>
    ggplot(
      aes(
        .time, F1
      )
    ) +
    geom_point() +
    labs(
      title = "DCT Smooth Data"
    )
}

Speaker Data

Description

Speaker Data

Usage

speaker_data

Format

speaker_data

A data frame with 10,697 rows and 8 columns

speaker

Speaker ID column

vowel

CMU Dictionary vowel class

plt_vclass

Modified Labov-Trager vowel class

ipa_vclas

IPA-like vowel class

word

Word that the vowel appeared in

F1, F2, F3

The first, second and third formants, in Hz

Speaker Tracks

Description

Speaker Tracks

Usage

speaker_tracks

Format

speaker_tracks

A data frame with 20,000 rows and 9 columns

speaker

Speaker ID column

id

Within speaker id for each token

vowel

CMU Dictionary vowel class

plt_vclass

Modified Labov-Trager vowel class

ipa_vclas

IPA-like vowel class

word

Word that the vowel appeared in

t

Measurement time point

F1, F2, F3

The first, second and third formants, in Hz