# Inverse DST (G Dataflow)

Version:

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

## DST{x}

The real input sequence.

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

## error in

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.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## x

The inverse DST of the real input sequence.

## error out

Error information.

The node produces this output 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.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm Definition for 1D Inverse DST

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

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

where

• N is the length of DST{x}
• yk is the kth element of DST{x}
• xn is the nth 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.

## Algorithm Definition for 2D Inverse DST

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

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

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:

1. Perform a one-dimensional inverse DST row-by-row on DST{x}. The output is Y'.
2. Perform a one-dimensional inverse DST column-by-column on Y'. The output is x.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application