Inverse FFT VI

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 f_i 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 f_i,j is the element in FFT {X}.

   The 2D Inverse Real FFT instance uses only the upper half part, from f_0,0 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.