dst

(Not recommended) Discrete sine transform

dst is not recommended.

Syntax

y = dst(x)

y = dst(x,n)

Description

y = dst(x) computes the discrete sine transform of x according to the equation

$$y(k)={\displaystyle \sum _{n=1}^{N}x(n)\sin \left(\pi \frac{kn}{N+1}\right)},k=1,\mathrm{...},N$$

If x is a matrix, then dst applies to each column. For best performance, the number of rows in x must be 2^m – 1, where m is an integer.

y = dst(x,n) truncates the vector x or pads it with trailing zeros to length n before computing the transform. If x is a matrix, then dst truncates or pads each column.

Examples

Discrete Sine Transform

Find the discrete sine transform of the exponential by using dst, and then invert the result by using idst.

Create a time vector sampled in increments of 0.1 second over a period of 10 seconds.

Ts = 0.1;
t = 0:Ts:10;

Compute and plot the exponential signal.

x = exp(t);
plot(t,x)
xlabel('Time (seconds)')
ylabel('Amplitude')

Compute the discrete sign transform of the signal, and create the vector f that corresponds to the sampling of the signal in frequency space.

y = dst(x);
fs = 1/Ts;
f = (0:length(y)-1)*fs/length(y);
plot(f,y)
xlabel('Frequency (Hz)')
ylabel('Magnitude')

Compute the inverse discrete sine transform of y, and plot the result.

z = idst(y);
figure
plot(t,z)
xlabel('Time (seconds)')
ylabel('Amplitude')

Input Arguments

x — Input array

vector | matrix

Input array, specified as a vector or a matrix. If x is a matrix, then dst applies to each column.

Data Types: double

n — Transform length

nonnegative integer

Transform length, specified as a nonnegative integer. If x is a vector, then dst truncates it or pads it with trailing zeros, so that the resulting vector has n elements. If x is a matrix, then dst truncates or pads each column.

Data Types: double

Output Arguments

y — Discrete sine transform coefficients

row vector | matrix

Discrete sine transform coefficients, returned as a vector or matrix of the same size as x.

Version History

Introduced before R2006a

R2016a: Not recommended

dst is not recommended. There are no plans to remove dst.