Discrete Fourier transform
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:
To compute the DFT of an input:
Starting in R2016b, instead of using the
to perform the operation defined by the System
object™, you can
call the object with arguments, as if it were a function. For example,
= step(obj,x) and
y = obj(x) perform
fft = dsp.FFT returns
H, that computes the
DFT of an N-D array. For column vectors or multidimensional
FFT object computes the DFT along the
first dimension. If the input is a row vector, the
computes a row of single-sample DFTs and issues a warning.
H = dsp.FFT(' returns a
with each property set to the specified value.
Specify the implementation used for the FFT as one of
Order of output elements relative to input elements
Designate order of output channel elements relative to order
of input elements. Set this property to
Divide butterfly outputs by two
Set this property to
The default value of this property is
Source of FFT length
Specify how to determine the FFT length as
Specify the FFT length. This property applies when you set the
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
Boolean value of wrapping or truncating input
Wrap input data when FFT length is shorter than input length.
If this property is set to true, modulo-length data wrapping occurs
before the FFT operation, given FFT length is shorter than the
input length. If this property is set to false, truncation of the
input data to the FFT length occurs before the FFT operation. The
|step||Discrete Fourier transform of input|
Find frequency components of a signal in additive noise.
Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent
step syntax. For example, myObject(x) becomes step(myObject,x).
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 ft = dsp.FFT('FFTLengthSource', 'Property', ... 'FFTLength', 1024); Y = ft(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)|');
Compute the FFT of a noisy sinusoidal input signal. The energy of the signal is stored as the magnitude square of the FFT coefficients. Determine the FFT coefficients which occupy 99.99% of the signal energy and reconstruct the time-domain signal by taking the IFFT of these coefficients. Compare the reconstructed signal with the original signal.
: If you are using R2016a or an earlier release, replace each call to the object with the equivalent
step syntax. For example,
Consider a time-domain signal , which is defined over the finite time interval . The energy of the signal is given by the following equation:
FFT Coefficients, are considered as signal values in the frequency domain. The energy of the signal in the frequency-domain is hence the sum of the squares of the magnitude of the FFT coefficients:
According to Parseval's theorem, the total energy of the signal in time or frequency-domain is the same.
dsp.SineWave System object to generate a sine wave sampled at 44.1 kHz and has a frequency of 1000 Hz. Construct a
dsp.IFFT objects to compute the FFT and the IFFT of the input signal.
The 'FFTLengthSource' property of each of these transform objects is set to 'Auto'. The FFT length is hence considered as the input frame size. The input frame size in this example is 1020, which is not a power of 2. Hence, select the 'FFTImplementation' as 'FFTW'.
L = 1020; Sineobject = dsp.SineWave('SamplesPerFrame',L,'PhaseOffset',10,... 'SampleRate',44100,'Frequency',1000); ft = dsp.FFT('FFTImplementation','FFTW'); ift = dsp.IFFT('FFTImplementation','FFTW','ConjugateSymmetricInput',true); rng(1);
Stream in the noisy input signal. Compute the FFT of each frame and determine the coefficients which constitute 99.99% energy of the signal. Take IFFT of these coefficients to reconstruct the time-domain signal.
numIter = 1000; for Iter = 1:numIter Sinewave1 = Sineobject(); Input = Sinewave1 + 0.01*randn(size(Sinewave1)); FFTCoeff = ft(Input); FFTCoeffMagSq = abs(FFTCoeff).^2; EnergyFreqDomain = (1/L)*sum(FFTCoeffMagSq); [FFTCoeffSorted, ind] = sort(((1/L)*FFTCoeffMagSq),1,'descend'); CumFFTCoeffs = cumsum(FFTCoeffSorted); EnergyPercent = (CumFFTCoeffs/EnergyFreqDomain)*100; Vec = find(EnergyPercent > 99.99); FFTCoeffsModified = zeros(L,1); FFTCoeffsModified(ind(1:Vec(1))) = FFTCoeff(ind(1:Vec(1))); ReconstrSignal = ift(FFTCoeffsModified); end
99.99% of the signal energy can be represented by the number of FFT coefficients given by
ans = 296
The signal is reconstructed efficiently using these coefficients. If you compare the last frame of the reconstructed signal with the original time-domain signal, you can see that the difference is very small and the plots match closely.
ans = 0.0431
plot(Input,'*'); hold on; plot(ReconstrSignal,'o'); hold off;
This object implements the algorithm, inputs, and outputs described on the FFT block reference page. The object properties correspond to the block parameters.
 FFTW (
 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.
Usage notes and limitations:
System Objects in MATLAB Code Generation (MATLAB Coder).
When the following conditions apply, the executable
generated from this System
object relies on prebuilt dynamic library
.dll files) included with MATLAB®:
FFTImplementation is set to
FFTImplementation is set to
not a power of two.
to package the code generated from this System
object and all
the relevant files in a compressed zip file. Using this zip file,
you can relocate, unpack, and rebuild your project in another development
environment where MATLAB is not installed. For more details,
see How To Run a Generated Executable Outside MATLAB.
When the FFT length is a power of two, you can generate standalone C and C++ code from this System object.