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dsp.IFFT System object

Package: dsp

Inverse discrete Fourier transform (IDFFT)


The IFFT object computes the inverse discrete Fourier transform (IDFFT) of the 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

  • Radix-2 decimation-in-time (DIT) algorithm

  • Radix-2 decimation-in-frequency (DIF) algorithm

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

To compute the IFFT of the input:

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

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

    Note:   Starting in R2016b, instead of using the step method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.


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

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



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.


Enable bit-reversed order interpretation of input elements

Set this property totrue if the order of Fourier transformed input elements to the IFFT object are in bit-reversed order. This property applies only when the FFTLengthSource property is Auto. The default is false, which denotes linear ordering.


Enable conjugate symmetric interpretation of input

Set this property to true if the input is conjugate symmetric to yield real-valued outputs. The discrete Fourier transform of a real valued sequence is conjugate symmetric, and setting this property to true optimizes the IDFT computation method. Setting this property to false for conjugate symmetric inputs may result in complex output values with nonzero imaginary parts. This occurs due to rounding errors. Setting this property to true for nonconjugate symmetric inputs results in invalid outputs. This property applies only when theFFTLengthSource property is Auto. The default is false.


Enable dividing output by FFT length

Specify whether to divide the IFFT output by the FFT length. The default is true and each element of the output is divided by the FFT length.


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. This property applies only when both the BitReversedInput and ConjugateSymmetricInput properties are false. The default is Auto.


FFT length

Specify the FFT length as a numeric scalar. This property applies when you set the BitReversedInput and ConjugateSymmetricInput properties to false, and 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 FFTImplementation property to Radix-2.

When you set the FFT implementation property to Radix-2, or when you set the BitReversedOutput property to true, this value must be a power of two.


Boolean value of wrapping or truncating input

Wrap input data when FFTLength is shorter than input length. If this property is set to true, modulo-length data wrapping occurs before the FFT operation, given FFTLength is shorter than the input length. If this property is set to false, truncation of the input data to the FFTLength occurs before the FFT operation. The default is true.

 Fixed-Point Properties


cloneCreate IFFT object with same property values
getNumInputsNumber of expected inputs to step method
getNumOutputsNumber of outputs of step method
isLockedLocked status for input attributes and nontunable properties
releaseAllow property value and input characteristics changes
stepInverse discrete Fourier transform of input


expand all

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).

This example analyzes the energy content in a sequence.

 Fs = 40; L = 128;
 t = (0:L-1)'/Fs;
 x = sin(2*pi*10*t) + 0.75*cos(2*pi*15*t);
 y = x + .5*randn(size(x)); % noisy signal
 hfft = dsp.FFT;
 hifft = dsp.IFFT('ConjugateSymmetricInput', true);
 X = hfft(x);
 [XX, ind] = sort(abs(X),1,'descend');
 XXn = sqrt(cumsum(XX.^2))/norm(XX);
 ii = find(XXn > 0.999, 1);
 disp('Number of FFT coefficients that represent 99.9% ')
 disp(['of the total energy in the sequence: ', num2str(ii)]);
 XXt = zeros(128,1);
 XXt(ind(1:ii)) = X(ind(1:ii));
 xt = hifft(XXt);
Number of FFT coefficients that represent 99.9% 
of the total energy in the sequence: 4

Verify that the reconstructed signal matches the original signal.

ans =



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

Output sampling mode parameter is not supported by dsp.IFFT.


[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.

See Also

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Introduced in R2012a

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