idst

(Not recommended) Invert discrete sine transform

idst is not recommended.

Syntax

x = idst(y)

x = idst(y,n)

Description

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

$$x(k)=\frac{2}{N+1}{\displaystyle \sum _{n=1}^{N}y(n)\sin \left(\pi \frac{kn}{N+1}\right)},k=1,\mathrm{...},N$$

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

x = idst(y,n) truncates the vector y or pads it with zeros to length n before computing the transform.

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

y — Input array

vector | matrix

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

Data Types: double

n — Transform length

nonnegative integer

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

Data Types: double

Output Arguments

x — Inverse discrete sine transform coefficients

vector | matrix

Inverse discrete sine transform coefficients, returned as a vector or matrix of the same size as y.

Version History

Introduced before R2006a

R2016a: Not recommended

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