Version:

Last Modified: March 15, 2017

Computes the inverse Discrete Sine Transform (DST) of a sequence.

The real input sequence.

This input can be a 1D or 2D array of double-precision, floating-point numbers.

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an **error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

**Default: **No error

The inverse DST of the real input sequence.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

If *y* represents a 1D array as the input sequence **DST{x}**, the one-dimensional inverse Discrete Sine Transform of *y* is defined as:

${x}_{n}=\frac{2}{N+1}\underset{k=0}{\overset{N-1}{\sum}}{y}_{k}\mathrm{sin}\frac{\pi (k+1)(n+1)}{N+1}$

where

*N*is the length of**DST{x}***y*_{k}is the*k*^{th}element of**DST{x}***x*_{n}is the*n*^{th}element of**x**

This node applies a fast inverse DST algorithm instead of calculating the inverse Discrete Sine Transform directly. This node implements the fast inverse DST algorithm using an FFT-based technique.

If *y* represents a 2D array as the input sequence **DST{x}**, the two-dimensional inverse Discrete Sine Transform of *y* is defined as:

$x(m,\text{\hspace{0.17em}}n)=\frac{2}{M+1}\frac{2}{N+1}\underset{u=0}{\overset{M-1}{\sum}}\underset{v=0}{\overset{N-1}{\sum}}y(u,\text{\hspace{0.17em}}v)\mathrm{sin}\frac{\pi (u+1)(u+1)}{N+1}\mathrm{sin}\frac{\pi (v+1)(v+1)}{M+1}$

where

*M*is the number of rows of**DST{x}***N*is the number of columns of**DST{x}**- x(m, n) is the element of the output matrix
**x**with row number*m*and column number*n* - y(u, v) is the element of
**DST{x}**with row number*u*and column number*v*

This node performs a two-dimensional inverse DST using the following two steps:

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: This product does not support FPGA devices