Obtain the coefficients of the discrete cosine transformation (DCTRUE).
dct(data, m = NULL, fit = FALSE)a vector or single column matrix of numeric values to which the 2nd order polynomial is to be fitted.
The number of DCT coefficients that are returned or on which the smoothed trajectory is based. Defaults to NULL which returns coefficients of frequencies k = 0, 1,2 .. N-1 where N is the length of the input signal, wav. If fit = TRUE and k = NULL, then the the sum of all the cosine waves whose amplitudes are the DCT coefficients are returned - which is equal to the original signal. k must be between 2 and the length of the signal.
if FALSE, return the DCT coefficients; if TRUE, the values of the smoothed trajectory are returned based on summing the cosine waves of the k lowest ordered DCT coefficients, where k is the argument given below.
Jonathan Harrington
The function calculates the DCT coefficients for any vector or single-columned matrix. The function can also be used to obtain a smoothed trajectory of the input data by summing the cosine waves derived from the first few DCT coefficients.
The algorithm first reflects the input signal about the last data point, N. Thus if the input signal vec if of length N, the algorithm creates a vector c(vec, rev(vec[-c(1,N)])). and the R fft function is applied to this reflected signal. The DCT coefficients are real part of what is returned by fft i.e. the amplitudes of the cosine waves of frequencies k = 0, 1, 2, ...2 *(N-1) radians per sample. The phase is zero in all cases. The amplitudes are calculated in such a way such that if these cosine waves are summed, the original (reflected) signal is reconstructed. What is returned by dct() are the amplitudes of the cosine waves (DCT coefficients) up to a frequency of N radians/sample, i.e. a vector of cosine wave amplitudes that has the same length as the original signal and of frequencies k = 0, 1, 2, ... (N-1). Alternatively, if fit=TRUE, a smoothed signal of the same length as the original signal is obtained based on a summation of the lowest ordered DCT coefficients. This dct() algorithm returns very similar values to DCT() with inv=FALSE written by Catherine Watson and used in Watson & Harrington (1999).
Watson, C. & Harrington, J. (1999). Acoustic evidence for dynamic formant trajectories in Australian English vowels. Journal of the Acoustical Society of America, 106, 458-468.
Zahorian, S., and Jagharghi, A. (1993). Spectral-shape features versus formants as acoustic correlates for vowels, Journal of the Acoustical Society of America, 94, 19661982.
plafit by
data(vowlax)
# obtain the first four DCT coefficients
# (frequencies k = 0, 1, 2, 3) for some
# first formant frequency data
vec <- vowlax.fdat[1,1]$data
dct(vec, m=4)
# obtain the corresponding smoothed
# trajectory
dct(vec, m=4 , fit=TRUE)
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