# 18.4.2 Inverse Fast Fourier Transform (IFFT)

IFFT is a fast algorithm to perform inverse (or backward) Fourier transform (IDFT), which undoes the process of DFT. IDFT of a sequence {$F_n$} that can be defined as:

$x_i=\frac{1}{N}\sum _{n=0}^{N-1}F_ne^{\frac{2\pi j}{N}ni}$

If an IFFT is performed on a complex FFT result computed by Origin, this will in principle transform the FFT result back to its original data set. However, this is true only when all of the following requirements are met:

• The Spectrum Type in FFT is two-sided.
• The Window option is Rectangle for both IFFT and FFT.
• The Factor option is the same for IFFT and FFT.
• If the Shift checkbox is selected in FFT, the Undo Shift Input Data checkbox must be selected in IFFT. Conversely, if the Shift checkbox is cleared in FFT, the Undo Shift Input Data checkbox should not be selected in IFFT.
 Note: The time sequence in the result of IFFT starts from zero. If the original data set does not start from zero, the time sequence generated by IFFT will be shifted from the original time sequence. However, the interval will be the same.

To use IFFT:

1. Make a workbook or a graph active.
2. Select Analysis: Signal Processing: FFT: IFFT from the Origin menu.
 Topics covered in this section: