1D FFT

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

for n = 0, 1, 2, …, 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:

where f_s is the sampling frequency.

The following table illustrates the pattern of the elements of FFT {X} for various FFT size and shift values, where Y is FFT {X} and n is the FFT size:

2D FFT

For 2D signals, the FFT VI computes the discrete Fourier transform (DFT) of the input matrix. This VI 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:

for u = 0, 1, …, M–1, v=0, 1, …, N–1

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

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

2D input signals	FFT without shift	FFT with shift

Related Information

Output Units for FFT-Based Vis

Examples

Refer to the following example files included with LabVIEW.

• labview\examples\Signal Processing\Transforms\FFT and Power Spectrum Units.vi