Created
July 31, 2025 11:32
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FFT for Google Sheets from 4o
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| class Complex { | |
| constructor(re, im) { | |
| this.re = re; | |
| this.im = im; | |
| } | |
| add(other) { | |
| return new Complex(this.re + other.re, this.im + other.im); | |
| } | |
| sub(other) { | |
| return new Complex(this.re - other.re, this.im - other.im); | |
| } | |
| mul(other) { | |
| return new Complex( | |
| this.re * other.re - this.im * other.im, | |
| this.re * other.im + this.im * other.re | |
| ); | |
| } | |
| } | |
| function fft(input) { | |
| const N = input.length; | |
| if (N <= 1) return input; | |
| const even = fft(input.filter((_, i) => i % 2 === 0)); | |
| const odd = fft(input.filter((_, i) => i % 2 !== 0)); | |
| const output = Array(N); | |
| for (let k = 0; k < N / 2; k++) { | |
| const angle = (-2 * Math.PI * k) / N; | |
| const twiddle = new Complex(Math.cos(angle), Math.sin(angle)).mul(odd[k]); | |
| output[k] = even[k].add(twiddle); | |
| output[k + N / 2] = even[k].sub(twiddle); | |
| } | |
| return output; | |
| } | |
| function fftFromRange(range) { | |
| const input = range.flat().map(x => new Complex(Number(x), 0)); | |
| const N = input.length; | |
| if ((N & (N - 1)) !== 0) throw new Error("Input length must be a power of 2"); | |
| const result = fft(input); | |
| return result.map(c => [c.re, c.im]); | |
| } |
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