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# dsp.IFFT System object

Package: dsp

Inverse discrete Fourier transform (IDFFT)

## Description

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.

## Construction

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.

## 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. BitReversedInput Enable bit-reversed order interpretation of input elements Set this property totrueif 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. ConjugateSymmetricInput 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. Normalize 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. 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. This property applies only when both the BitReversedInput and ConjugateSymmetricInput properties are false. The default is Auto. FFTLength 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.

## Methods

 clone Create IFFT 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 Inverse discrete Fourier transform of input

## Examples

Use DFT and IDFT to analyze 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 = step(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 = step(hifft, XXt);
% Verify the reconstructed signal matches the original
norm(x-xt) ```

## Algorithms

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.

## 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.

## See Also

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