Parallel Fast Fourier Transform Literature Review

The fast Fourier transform (FFT), developed in 1965, is widely considered one of the most prolific and significant algorithms of the 20th century. While the classic Fourier Transform algorithm converts data from timedomain to frequency domain in O(N), the FFT reduces the complexity to O(NlgN). This performance improvement has had a significant impact on many fields and has revolutionized the areas of digital signal processing and numerical convolution. Since the FFT was introduced, a wide range of research has attempted to leverage and improve on the idea. One of the largest trends was in attempting to parallelize the FFT to further improve its performance. Despite the wealth of research, the basic FFT algorithm remains mostly unchanged over the near half-decade since. This paper presents an overview of the research centered around the Fast Fourier Transform, with a focus on parallelization. We review the works that led to major contributions to the field and discuss how the field has evolved over the years.