Is FFT reversible?

The transformation from the time domain to the frequency domain is reversible.

What is Radix 4 FFT?

The radix-4 DIF FFT divides an N-point discrete Fourier transform (DFT) into four N 4 -point DFTs, then into 16 N 16 -point DFTs, and so on. In the radix-2 DIF FFT, the DFT equation is expressed as the sum of two calculations. The following equations illustrate radix-4 decimation in frequency.

Why is the bit reversal in FFT called bit reversal?

The shuffling of the input data is known as bit reversal because the scrambled order of the input data index can be obtained by reversing the bits of the binary representation of the normal input data index order. Sounds confusing, but it’s really not—Table 4-1 illustrates the input index bit reversal for our 8-point FFT example.

Why is bit reversal important in radix 2 Cooley-Tukey FFT?

{\\displaystyle \\lfloor n/4floor } positions. Bit reversal is most important for radix-2 Cooley–Tukey FFT algorithms, where the recursive stages of the algorithm, operating in-place, imply a bit reversal of the inputs or outputs. Similarly, mixed-radix digit reversals arise in mixed-radix Cooley–Tukey FFTs.

How to find the next bit reversal address?

To find the next bit-reversal address, you simply add N/2 to the present address, from left to right (not our usual right-to-left addition). Consider the case as in the image given by Matt’s answer, N = 8. that corresponds to 1000. Therefore, N/2 = 4 = 100.

When to use reverse order in FFT Stack Exchange?

Like I want to only for the when the index is odd because that involve some reverse carry propagation, but when the index is even you just add N/2 to it to get your reverse index r. An example of N=8 would be perfect if someone can explain me. If I understand your question correctly you want this (index | binary | bit rev. | bit rev. index):