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73 lines
2.0 KiB
C++
73 lines
2.0 KiB
C++
/*This is a C++ Program to perform Fast Fourier Transform. A fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier transform (DFT) and its inverse. Fourier analysis converts time (or space) to frequency and vice versa; an FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors.*/
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#include <iostream>
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#include <complex>
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#include <cmath>
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#include <iterator>
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using namespace std;
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unsigned int bitReverse(unsigned int x, int log2n)
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{
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int n = 0;
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int mask = 0x1;
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for (int i = 0; i < log2n; i++)
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{
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n <<= 1;
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n |= (x & 1);
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x >>= 1;
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}
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return n;
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}
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const double PI = 3.1415926536;
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template<class Iter_T>
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void fft(Iter_T a, Iter_T b, int log2n)
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{
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typedef typename iterator_traits<iter_t>::value_type complex;
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const complex J(0, 1);
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int n = 1 << log2n;
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for (unsigned int i = 0; i < n; ++i)
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{
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b[bitReverse(i, log2n)] = a[i];
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}
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for (int s = 1; s <= log2n; ++s)
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{
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int m = 1 << s;
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int m2 = m >> 1;
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complex w(1, 0);
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complex wm = exp(-J * (PI / m2));
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for (int j = 0; j < m2; ++j)
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{
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for (int k = j; k < n; k += m)
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{
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complex t = w * b[k + m2];
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complex u = b[k];
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b[k] = u + t;
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b[k + m2] = u - t;
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}
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w *= wm;
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}
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}
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}
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int main(int argc, char **argv)
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{
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typedef complex cx;
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cx a[] = { cx(0, 0), cx(1, 1), cx(3, 3), cx(4, 4), cx(4, 4), cx(3, 3), cx(
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1, 1), cx(0, 0)
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};
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cx b[8];
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fft(a, b, 3);
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for (int i = 0; i < 8; ++i)
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cout << b[i] << "\n";
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}
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/*
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(16,16)
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(-4.82843,-11.6569)
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(0,0)
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(-0.343146,0.828427)
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(0,0)
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(0.828427,-0.343146)
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(0,0)
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(-11.6569,-4.82843)
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