# dst, idst

Discrete sine transform

## Syntax

`y = dst(x)y = dst(x,n)x = idst(y)x = idst(y,n)`

## Description

The `dst` function implements the following equation:

$y\left(k\right)=\sum _{n=1}^{N}x\left(n\right)\mathrm{sin}\left(\pi \frac{kn}{N+1}\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}k=1,...,N.$

`y = dst(x)` computes the discrete sine transform of the columns of `x`. For best performance speed, the number of rows in `x` should be 2m – 1, for some integer m.

`y = dst(x,n)` pads or truncates the vector `x` to length `n` before transforming.

If `x` is a matrix, the `dst` operation is applied to each column.

The `idst` function implements the following equation:

`x = idst(y)` calculates the inverse discrete sine transform of the columns of `y`. For best performance speed, the number of rows in `y` should be 2m – 1, for some integer m.

`x = idst(y,n)` pads or truncates the vector `y` to length `n` before transforming.

If `y` is a matrix, the `idst` operation is applied to each column.

For more information about this algorithm, see Solve Poisson's Equation on a Grid.

## See Also

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