Inverse FFT VI

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Requires: Full Development System

Computes the inverse discrete Fourier transform (IDFT) of the input sequence FFT {X}. You must manually select the polymorphic instance you want to use.

Details  

Use the pull-down menu to select an instance of this VI.

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Inverse Real FFT

FFT {X} is the complex valued input sequence, which should be conjugated centrosymmetric except for the first element. This instance uses only the anterior half of FFT {X}.
shift? specifies whether the DC component is at the center of FFT {X}. The default is FALSE.
X is the inverse real FFT of FFT{X}.
error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Inverse Complex FFT

FFT {X} is the complex valued input sequence.
shift? specifies whether the DC component is at the center of FFT {X}. The default is FALSE.
X is the inverse complex FFT of FFT{X}.
error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

2D Inverse Real FFT

FFT {X} is the complex valued input sequence, which should be conjugated centrosymmetric except for the first row and column. This instance uses only the upper half of FFT {X}.
shift? specifies whether the DC component is at the center of FFT {X}. The default is FALSE.
X is the inverse real FFT of FFT{X}.
error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

2D Inverse Complex FFT

FFT {X} is the complex valued input sequence.
shift? specifies whether the DC component is at the center of FFT {X}. The default is FALSE.
X is the inverse complex FFT of FFT {X}.
error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Inverse FFT Details

Use the Inverse Real FFT and the 2D Inverse Real FFT instances of this VI only if FFT {X} is the Fourier transform of a real time-domain signal. Otherwise, use the Inverse Complex FFT and the 2D Inverse Complex FFT instances. When FFT {X} is the Fourier transform of a real time-domain signal, FFT {X} is conjugated centrosymmetric, and the Inverse Real FFT and the 2D Inverse Real FFT instances use only the anterior part of FFT{X}.

The following formulas show the conjugated centrosymmetric property of FFT {X} when FFT {X} is the Fourier transform of a real time-domain signal and shift? is false.

  1. When FFT {X} is the Fourier transform of a 1D real time-domain signal with length N, the posterior half part of FFT {X} can be constructed by the anterior half part. The centrosymmetric relationship between the anterior and posterior half part of FFT {X} can be written as

    ,

    where fi is the element in FFT {X}.

    The Inverse Real FFT instance VI uses only the anterior half part, from f0 to f_ to perform the inverse real FFT, where means the floor operation.

  2. When FFT {X} is the Fourier transform of a 2D real time-domain signal with M rows and N columns, the lower half part of FFT {X} can be constructed by the upper half part. The centrosymmetric relationship between the upper and lower half part of FFT {X} can be written as

    where fi,j is the element in FFT {X}.

    The 2D Inverse Real FFT instance uses only the upper half part, from f0,0 to f_ to perform the 2D inverse real FFT, where means the floor operation.

This VI computes the inverse discrete Fourier transform (IDFT) of a vector or matrix FFT {X} with a fast Fourier transform algorithm. The shift? input specifies whether the input FFT {X} is a DC-centered FFT.

For a 1D, N-sample, frequency domain sequence Y, the IDFT is defined as:

for n = 0, 1, 2, …, N–1.

For a 2D, M-by-N frequency domain array Y, the IDFT is defined as:

for m = 0, 1, …, M–1, n=0, 1, …, N–1.