Bit-reversal permutation

Bit-reversal permutation is a mathematical operation typically used in computer science and signal processing, particularly in the context of algorithms such as the Fast Fourier Transform (FFT). The basic idea is to permute the order of bits in binary representations of numbers. ### Definition Given an integer \( n \), the bit-reversal permutation rearranges the integers in the range \( 0 \) to \( n-1 \) by reversing the bits of their binary representations.