# FFT (G Dataflow)

Computes the fast Fourier transform (FFT) of a sequence.

## reset

A Boolean that specifies whether to reset the internal state of the node.

 True Resets the internal state of the node. False Does not reset the internal state of the node.

This input is available only if you wire a double-precision, floating-point number or a complex double-precision, floating-point number to x.

Default: False

## x

Input signal.

This input accepts the following data types:

• Double-precision, floating-point number
• Complex double-precision, floating-point number
• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers
• 2D array of double-precision, floating-point numbers
• 2D array of complex double-precision, floating-point numbers

## FFT size

Length of the FFT you want to perform.

This input changes to m if you wire a 2D array of double-precision, floating-point numbers or a 2D array of complex double-precision, floating-point numbers to x.

Node Behavior When x is a 1D Array of Numbers

When you wire a 1D array of double-precision, floating-point numbers or a 1D array of complex double-precision, floating-point numbers to x, if FFT size is greater than the number of elements in x, this node adds zeros to the end of x to match the size of FFT size. If FFT size is less than the number of elements in x, this node uses only the first n elements in x to perform the FFT, where n is FFT size. If FFT size is less than or equal to 0, this node uses the length of x as the FFT size.

Node Behavior When x is a Single Data Point

When you wire a double-precision, floating-point number or a complex double-precision, floating-point number to x, if FFT size is greater than sample length, this node collects data according to sample length but adds zeros to the end of the data set to match the size of FFT size. If FFT size is less than sample length, this node ignores sample length and uses only the first n elements in the data set to perform the FFT, where n is FFT size. If FFT size is less than or equal to 0, this node uses sample length as the FFT size.

Default: -1

## m

Number of rows of the 2D FFT. This node truncates or zero-pads x to an m × n array before performing the FFT.

This input is available only if you wire a 2D array of double-precision, floating-point numbers or a 2D array of complex double-precision, floating-point numbers to x.

Default: -1

## sample length

Length of each set of data. The node performs computation for each set of data.

sample length must be greater than zero.

This input is available only if you wire a double-precision, floating-point number or a complex double-precision, floating-point number to x.

Default: 100

## n

Number of columns of the 2D FFT. This node truncates or zero-pads x to an m × n array before performing the FFT.

This input is available only if you wire a 2D array of double-precision, floating-point numbers or a 2D array of complex double-precision, floating-point numbers to x.

Default: -1

## shift?

A Boolean that determines whether the DC component is at the center of the FFT of the input sequence.

 True The DC component is at the center of the FFT{x}. False The DC component is not at the center of the FFT{x}.

This input is available only if you wire one of the following data types to x:

• 1D array of double-precision, floating-point numbers
• 1D array of complex double-precision, floating-point numbers
• 2D array of double-precision, floating-point numbers
• 2D array of complex double-precision, floating-point numbers

How This Input Affects 1D FFT

The following table illustrates the pattern of the elements of FFT{x} with various length of the FFT, when shift? is False. Y is FFT{x} and n is the length of the FFT:

n is even (k = n/2) n is odd (k = (n-1)/2)
Array Element Corresponding Frequency Array Element Corresponding Frequency
Y 0 DC component Y 0 DC component
Y 1 Δf Y 1 Δf
Y 2 f Y 2 f
Y 3 f Y 3 f
$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$
Y k-2 (k - 2)Δf Y k-2 (k - 2)Δf
Y k-1 (k - 1)Δf Y k-1 (k - 1)Δf
Y k Nyquist Frequency Y k kΔf
Y k+1 -(k - 1)Δf Y k+1 -kΔf
Y k+2 -(k - 2)Δf Y k+2 -(k - 1)Δf
$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$
Y n-3 -3Δf Y n-3 -3Δf
Y n-2 -2Δf Y n-2 -2Δf
Y n-1 f Y n-1 f

The following table illustrates the pattern of the elements of FFT{x} with various length of the FFT, when shift? is True. Y is FFT{x} and n is the length of the FFT:

n is even (k = n/2) n is odd (k = (n-1)/2)
Array Element Corresponding Frequency Array Element Corresponding Frequency
Y 0 -(Nyquist Frequency) Y 0 -kΔf
Y 1 -(k - 1)Δf Y 1 -(k - 1)Δf
Y 2 -(k - 2)Δf Y 2 -(k - 2)Δf
Y 3 -(k - 3)Δf Y 3 -(k - 3)Δf
$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$
Y k-2 -2Δf Y k-2 -2Δf
Y k-1 f Y k-1 f
Y k DC component Y k DC component
Y k+1 Δf Y k+1 Δf
Y k+2 f Y k+2 f
$\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$ $\begin{array}{c}\cdot \\ \cdot \\ \cdot \end{array}$
Y n-3 (k - 3)Δf Y n-3 (k - 2)Δf
Y n-2 (k - 2)Δf Y n-2 (k - 1)Δf
Y n-1 (k - 1)Δf Y n-1 kΔf

How This Input Affects 2D FFT

The illustration below shows the effect of shift? on the 2D FFT result:

2D input signals FFT without shift FFT with shift

Default: False

## 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

## FFT{x}

FFT of the input signal.

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

## 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 FFT

For 1D signals, this node computes the discrete Fourier transform (DFT) of the input sequence with a fast Fourier transform algorithm. The 1D DFT is defined as:

${Y}_{k}=\sum _{n=0}^{N-1}{x}_{n}{e}^{-j2\pi kn/N}\text{}\text{}\text{}\mathrm{for}\text{}n=0,\text{}1,\text{}2,\text{}...,\text{}N-1$

where x is the input sequence, N is the number of elements of x, and Y is the transform result.

The frequency resolution, or the frequency spacing between the components of Y, is:

$\mathrm{\Delta }f=\frac{{f}_{s}}{N}$

where f s is the sampling frequency.

## Algorithm Definition for 2D FFT

For 2D signals, this node computes the discrete Fourier transform (DFT) of the input matrix. This node performs a 1D FFT on the rows of the input matrix and then performs a 1D FFT on the columns of the output of the preceding step. The DFT of an M-by-N matrix is defined as:

$Y\left(u,v\right)=\sum _{m=0}^{M-1}\sum _{n=0}^{N-1}x\left(m,n\right){e}^{-j2\pi mu/M}{e}^{-j2\pi nv/N}\text{}\text{}\text{}\mathrm{for}\text{}\text{}u=0,\text{}1,\text{}...,\text{}M-1,\text{}v=0,\text{}1,\text{}...,\text{}N-1$

where x is the input matrix and Y is the transform result.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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