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# dsp.FFT System object

Package: dsp

Discrete Fourier transform

## Description

The FFT object computes the discrete Fourier transform (DFT) of an input. The object uses one or more of the following fast Fourier transform (FFT) algorithms depending on the complexity of the input and whether the output is in linear or bit-reversed order:

• Double-signal algorithm

• Half-length algorithm

• An algorithm chosen by FFTW [1], [2]

To compute the DFT of an input:

1. Define and set up your FFT object. See Construction.

2. Call step to compute the DFT of the input according to the properties of dsp.FFT. The behavior of step is specific to each object in the toolbox.

## Construction

H = dsp.FFT returns a FFT object, H, that computes the DFT of an N-D array. For column vectors or multidimensional arrays, the FFT object computes the DFT along the first dimension. If the input is a row vector, the FFT object computes a row of single-sample DFTs and issues a warning.

H = dsp.FFT('PropertyName',PropertyValue, ...) returns a FFT object, H, with each property set to the specified value.

## Properties

 FFTImplementation FFT implementation Specify the implementation used for the FFT as one of Auto | Radix-2 | FFTW. When you set this property to Radix-2, the FFT length must be a power of two. BitReversedOutput Order of output elements relative to input elements Designate order of output channel elements relative to order of input elements. Set this property to true to output the frequency indices in bit-reversed order. The default is false, which corresponds to a linear ordering of frequency indices. Normalize Divide butterfly outputs by two Set this property to true if the output of the FFT should be divided by the FFT length. This option is useful when you want the output of the FFT to stay in the same amplitude range as its input. This is particularly useful when working with fixed-point data types. The default value of this property is false with no scaling. FFTLengthSource Source of FFT length Specify how to determine the FFT length as Auto or Property. When you set this property to Auto, the FFT length equals the number of rows of the input signal. The default is Auto. FFTLength FFT length Specify the FFT length. This property applies when you set the FFTLengthSource property to Property. The default is 64. This property must be a power of two when the input is a fixed-point data type, or when you set the BitReversedOutput property to true, or when you set the FFTImplementation property to Radix-2.

## Methods

 clone Create FFT object with same property values getNumInputs Number of expected inputs to step method getNumOutputs Number of outputs of step method isLocked Locked status for input attributes and nontunable properties release Allow property value and input characteristics changes step Discrete Fourier transform of input

## Examples

Find frequency components of a signal in additive noise:

Fs = 800; L = 1000;
t = (0:L-1)'/Fs;
x = sin(2*pi*250*t) + 0.75*cos(2*pi*340*t);
y = x + .5*randn(size(x)); % noisy signal

hfft = dsp.FFT('FFTLengthSource', 'Property', ...
'FFTLength', 1024);

Y = step(hfft, y);

% Plot the single-sided amplitude spectrum
plot(Fs/2*linspace(0,1,512), 2*abs(Y(1:512)/1024));
title('Single-sided amplitude spectrum of noisy signal y(t)');
xlabel('Frequency (Hz)'); ylabel('|Y(f)|');

## Algorithms

This object implements the algorithm, inputs, and outputs described on the FFT block reference page. The object properties correspond to the block parameters.

## References

[1] FFTW (http://www.fftw.org)

[2] Frigo, M. and S. G. Johnson, "FFTW: An Adaptive Software Architecture for the FFT,"Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Vol. 3, 1998, pp. 1381-1384.