快速傅里叶变换
将时域信号转化为频域频谱图的数学算法，是音频识别和信号处理的核心工具，最早由约瑟夫·傅里叶于19世纪提出理论基础
Core Facts
Timeline (last 90 days)
The conversation mentioned OpenAI's improved results on the fast Fourier transform, and the phenomenon of people on Twitter接力 improving constants in relay.
The Schönhage-Strassen algorithm transforms integer multiplication into polynomial multiplication and performs computation over a ring using the FFT.
The new algorithm constructs special moduli to perform exact multiplication at smaller lengths, optimizing the zero-padding step in traditional FFT multiplication.
The number theoretic transform (NTT) is a variant of the fast Fourier transform (FFT) over finite fields or integer modulus rings, free of the precision errors caused by floating-point operations.
Toom-Cook and the FFT-based Schönhage-Strassen algorithm further approach n log n.
In 1971, Schönhage and Strassen introduced the fast Fourier transform (FFT), pushing the complexity of integer multiplication down to O(n log n log log n).
The Fast Fourier Transform reduces the computational complexity of the DFT from the naive O(N²) to O(N log N).
All Facts (7)
The Fast Fourier Transform reduces the computational complexity of the DFT from the naive O(N²) to O(N log N).
65%UnverifiedThe Schönhage-Strassen algorithm transforms integer multiplication into polynomial multiplication and performs computation over a ring using the FFT.
50%UnverifiedThe new algorithm constructs special moduli to perform exact multiplication at smaller lengths, optimizing the zero-padding step in traditional FFT multiplication.
50%UnverifiedThe number theoretic transform (NTT) is a variant of the fast Fourier transform (FFT) over finite fields or integer modulus rings, free of the precision errors caused by floating-point operations.
50%UnverifiedIn 1971, Schönhage and Strassen introduced the fast Fourier transform (FFT), pushing the complexity of integer multiplication down to O(n log n log log n).
50%UnverifiedToom-Cook and the FFT-based Schönhage-Strassen algorithm further approach n log n.
50%UnverifiedThe conversation mentioned OpenAI's improved results on the fast Fourier transform, and the phenomenon of people on Twitter接力 improving constants in relay.
50%