# Inverse DCT (G Dataflow)

Computes the inverse Discrete Cosine Transform (DCT) of a sequence.

## DCT{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 DCT 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 DCT

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

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

and

${\alpha }_{k}=\left\{\begin{array}{c}\frac{1}{\sqrt{2}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}k=0\\ 1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}k=1,\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}...,\text{\hspace{0.17em}}N-1\end{array}$

where

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

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

## Algorithm Definition for 2D Inverse DCT

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

$x\left(m,n\right)=\sqrt{\frac{2}{M}}\sqrt{\frac{2}{N}}\underset{u=0}{\overset{M-1}{\sum }}\underset{v=0}{\overset{N-1}{\sum }}{\alpha }_{u}{\alpha }_{v}y\left(u,v\right)\mathrm{cos}\frac{\left(2m+1\right)u\pi }{2M}\mathrm{cos}\frac{\left(2n+1\right)v\pi }{2N}$

where

• M is the number of rows of DCT{x}
• N is the number of columns of DCT{x}
• x(m, n) is the element of x with row number m and column number n
• y(u, v) is the element of DCT{x} with row number u and column number v

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

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