Fast Algorithm for DFT (Discrete Fourier Transform)

In this article, "Radix-2 FFT" refers to a fast algorithm for the Discrete Fourier Transform (DFT), which significantly reduces computational time and enhances efficiency. The algorithm works by decomposing the DFT into smaller DFTs using a divide-and-conquer approach, while utilizing twiddle factors for phase adjustments. This decomposition is typically implemented recursively or iteratively, with the most common implementation involving bit-reversal permutation and butterfly operations. Key functions in the algorithm include complex multiplication with twiddle factors and combining results from smaller DFTs. This makes it highly valuable in numerous applications such as digital signal processing and image processing. Furthermore, Radix-2 FFT is widely used in audio compression and encoding due to its ability to provide high-quality data compression and decompression. The algorithm's efficiency stems from reducing the computational complexity from O(N²) to O(N log N). In summary, Radix-2 FFT is a powerful algorithm that plays a crucial role in modern computer science and technology.