dst: Discrete Sine Transform

In gjmvanboxtel/gsignal: Signal Processing

Discrete Sine Transform

Description

Compute the discrete sine transform of a signal.

Usage

dst(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).

Details

The discrete sine transform (DST) is closely related to the discrete Fourier transform. but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length.

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

The 'Matlab' documentation for the DST warns that the use of the function is not recommended. They do not state the reason why, but it is likely that use of the discrete cosine transform (DCT)is preferred for image processing. Because cos(0) is 1, the first coefficient of the DCT (II) is the mean of the values being transformed. This makes the first coefficient of each 8x8 block represent the average tone of its constituent pixels, which is obviously a good start. Subsequent coefficients add increasing levels of detail, starting with sweeping gradients and continuing into increasingly fiddly patterns, and it just so happens that the first few coefficients capture most of the signal in photographic images. Sin(0) is 0, so the DSTs start with an offset of 0.5 or 1, and the first coefficient is a gentle mound rather than a flat plain. That is unlikely to suit ordinary images, and the result is that DSTs require more coefficients than DCTs to encode most blocks. This explanation was provided by Douglas Bagnall on Stackoverflow.

Value

Discrete sine transform, returned as a vector or matrix.

Author(s)

Paul Kienzle, [e-mail].
Conversion to R by Geert van Boxtel, [e-mail].

References

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

See Also

idst

Examples

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

gjmvanboxtel/gsignal documentation built on Nov. 22, 2023, 8:19 p.m.