Inverse discrete cosine transform

Reconstruct curve coordinates from discrete cosine transform coefficients.

Usage

dct_i(x, nb_h = NULL, nb_pts = 60, ..., .cols = NULL, .name = "_i")

Arguments

x

A numeric vector, list (from raw dct), list of vectors, or tibble with coe columns.

nb_h

Integer. Number of harmonics to use for reconstruction. If NULL, uses all available harmonics.

nb_pts

Integer. Number of points to reconstruct. Default is 60.

...

Additional arguments (reserved for future use).

.cols

Column name(s) to process when x is a tibble. If NULL, processes all coe columns automatically.

.name

Character. Name suffix for output curve columns when x is a tibble. Default is "_i". Output columns will be named originalname_i.

Value

• If x is a vector or raw list: returns a matrix (nb_pts x 2) with class "xy"

• If x is a list of vectors: returns a list of matrices

• If x is a tibble: returns the tibble with new cur column(s) added

Details

Performs inverse discrete cosine transform to reconstruct curve coordinates from coefficients. This is useful for:

• Visualizing shapes at different harmonic levels

• Reconstructing shapes from PCA or other statistical analyses

• Filtering out high-frequency noise by using fewer harmonics

If nb_h is less than the total number of harmonics in the coefficients, only the first nb_h harmonics are used (low-pass filtering).

See also

dct() for forward transform

Examples

# Single curve
data(olea)
cur <- olea$VD[[1]]
coefs <- dct(cur, nb_h = 12)

# Reconstruct with all harmonics
cur_reconstructed <- dct_i(coefs)

# Reconstruct with fewer harmonics (smoothing)
cur_smooth <- dct_i(coefs, nb_h = 6)

# From raw output
coefs_raw <- dct(cur, raw = TRUE)
dct_i(coefs_raw)
#> <xy [60 x 2]>
#>       x      y     
#>  [1,] -0.500  0.000
#>  [2,] -0.486  0.008
#>  [3,] -0.462  0.023
#>  [4,] -0.432  0.043
#>  [5,] -0.401  0.065
#>  [6,] ...    ...   
#>  [7,] 0.521  0.065 
#>  [8,] 0.518  0.043 
#>  [9,] 0.512  0.023 
#> [10,] 0.505  0.008 
#> [11,] 0.500  0.000 

if (FALSE) { # \dontrun{
# Tibble workflow
library(dplyr)
olea %>%
  dct(.cols = VD) %>%
  dct_i()  # Creates VD_coe_i

# Custom column names
olea %>%
  dct(.cols = VD) %>%
  dct_i(.cols = VD_coe, .name = "VD_reconstructed")
} # }