 # C++ Programming Code Examples

## C++ > Mathematics Code Examples

### Compute Discrete Fourier Transform Using the Fast Fourier Transform Approach

``` Compute Discrete Fourier Transform Using the Fast Fourier Transform Approach 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. #include <iostream> #include <complex> #include <cmath> #include <iterator> using namespace std; unsigned int bitReverse(unsigned int x, int log2n) { int n = 0; int mask = 0x1; for (int i = 0; i < log2n; i++) { n <<= 1; n |= (x & 1); x >>= 1; } return n; } const double PI = 3.1415926536; template<class Iter_T> void fft(Iter_T a, Iter_T b, int log2n) { typedef typename iterator_traits<iter_t>::value_type complex; const complex J(0, 1); int n = 1 << log2n; for (unsigned int i = 0; i < n; ++i) { b[bitReverse(i, log2n)] = a[i]; } for (int s = 1; s <= log2n; ++s) { int m = 1 << s; int m2 = m >> 1; complex w(1, 0); complex wm = exp(-J * (PI / m2)); for (int j = 0; j < m2; ++j) { for (int k = j; k < n; k += m) { complex t = w * b[k + m2]; complex u = b[k]; b[k] = u + t; b[k + m2] = u - t; } w *= wm; } } } int main(int argc, char **argv) { typedef complex cx; cx a[] = { cx(0, 0), cx(1, 1), cx(3, 3), cx(4, 4), cx(4, 4), cx(3, 3), cx( 1, 1), cx(0, 0) }; cx b; fft(a, b, 3); for (int i = 0; i < 8; ++i) cout << b[i] << "\n"; } ``` 