dct function

Discrete Cosine Transform

Compute the unitary discrete cosine transform of a signal.

dct(x, n = NROW(x))

Arguments

• x: input data, specified as a numeric vector or matrix. In case of a vector it represents a single signal; in case of a matrix each column is a signal.
• n: transform length, specified as a positive integer scalar. Default: NROW(x).

Returns

Discrete cosine transform, returned as a vector or matrix.

Details

The discrete cosine transform (DCT) is closely related to the discrete Fourier transform. You can often reconstruct a sequence very accurately from only a few DCT coefficients. This property is useful for applications requiring data reduction.

The DCT has four standard variants. This function implements the DCT-II according to the definition in [1], which is the most common variant, and the original variant first proposed for image processing.

Note

The transform is faster if x is real-valued and has even length.

Examples

x <- matrix(seq_len(100) + 50 * cos(seq_len(100) * 2 * pi / 40))
X <- dct(x)

# Find which cosine coefficients are significant (approx.)
# zero the rest
nsig <- which(abs(X) < 1)
N <- length(X) - length(nsig) + 1
X[nsig] <- 0

# Reconstruct the signal and compare it to the original signal.
xx <- idct(X)
plot(x, type = "l")
lines(xx, col = "red")
legend("bottomright", legend = c("Original", paste("Reconstructed, N =", N)),
       lty = 1, col = 1:2)

References

[1] https://en.wikipedia.org/wiki/Discrete_cosine_transform

See Also

idct

Author(s)

Paul Kienzle, pkienzle@users.sf.net .

Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com .