mirror of
https://hub.njuu.cf/TheAlgorithms/C-Plus-Plus.git
synced 2023-10-11 13:05:55 +08:00
123 lines
3.1 KiB
C++
123 lines
3.1 KiB
C++
/**
|
|
* @fast_fourier_transform.cpp
|
|
* @brief A fast Fourier transform (FFT) is an algorithm that computes the
|
|
* discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT).
|
|
* @details
|
|
* https://medium.com/@aiswaryamathur/understanding-fast-fourier-transform-from-scratch-to
|
|
-solve-polynomial-multiplication-8018d511162f
|
|
* @author [Ameya Chawla](https://github.com/ameyachawlaggsipu)
|
|
*/
|
|
|
|
#include<iostream>//Standard Library for input and output
|
|
#include<cmath>//For sine,cosine functions
|
|
#include<complex>//For storing points and coefficents
|
|
#include <cassert>//For Assertions
|
|
# define pi 3.14159265358979323846
|
|
using namespace std;
|
|
|
|
/**
|
|
* @brief FastFourierTransform is a recursive function which returns list of complex numbers
|
|
* @param p List of Coefficents in form of complex numbers
|
|
* @param n Count of elements in list p
|
|
* @returns p if n==1
|
|
* @returns y if n!=1
|
|
*/
|
|
|
|
complex<double>* FastFourierTransform(complex<double>*p,int n)
|
|
{
|
|
|
|
if(n==1) return p; ///Base Case To return
|
|
|
|
complex<double> om=complex<double>(cos(2*pi/n),sin(2*pi/n)); ///Calculating value of omega
|
|
|
|
complex<double> *pe= new complex<double>[n/2]; /// Coefficents of even power
|
|
|
|
complex<double> *po= new complex<double>[n/2]; ///Coefficents of odd power
|
|
|
|
int k1=0,k2=0;
|
|
for(int j=0;j<n;j++)
|
|
{
|
|
if(j%2==0){
|
|
pe[k1++]=p[j]; ///Assigning values of even coefficents
|
|
|
|
}
|
|
else po[k2++]=p[j]; ///Assigning value of odd coefficents
|
|
|
|
|
|
}
|
|
|
|
complex<double>*ye=FastFourierTransform(pe,n/2);///Recursive Call
|
|
|
|
complex<double>*yo=FastFourierTransform(po,n/2);///Recursive Call
|
|
|
|
complex<double>*y=new complex<double>[n];///Final value representation list
|
|
|
|
|
|
for(int i=0;i<n/2;i++)
|
|
{
|
|
y[i]=ye[i]+pow(om,i)*yo[i]; ///Updating the first n/2 elements
|
|
y[i+n/2]=ye[i]-pow(om,i)*yo[i];///Updating the last n/2 elements
|
|
}
|
|
|
|
return y;///Return the list
|
|
|
|
}
|
|
|
|
/**
|
|
* @brief Self-test implementations
|
|
* @returns void
|
|
*/
|
|
static void test() {
|
|
/* descriptions of the following test */
|
|
|
|
complex<double> t1[2]={1,2};///Test case 1
|
|
|
|
complex<double> t2[4]={1,2,3,4};///Test case 2
|
|
|
|
|
|
|
|
int n1=sizeof(t1)/sizeof(complex<double>);
|
|
int n2=sizeof(t2)/sizeof(complex<double>);
|
|
|
|
|
|
complex<double> r1[2]={{3,0},{-1,0} };///True Answer for test case 1
|
|
|
|
complex<double> r2[4]={{10,0},{-2,-2},{-2,0},{-2,2} };///True Answer for test case 2
|
|
|
|
|
|
complex<double> *o1=FastFourierTransform(t1,n1);
|
|
complex<double> *o2=FastFourierTransform(t2,n2);
|
|
|
|
|
|
for(int i=0;i<n1;i++)
|
|
{
|
|
assert(r1[i].real()-o1->real()<0.000000000001 and r1[i].imag()-o1->imag()<0.000000000001 );
|
|
o1++;
|
|
}
|
|
|
|
for(int i=0;i<n2;i++)
|
|
{
|
|
assert(r2[i].real()-o2->real()<0.000000000001 and r2[i].imag()-o2->imag()<0.000000000001 );
|
|
o2++;
|
|
}
|
|
|
|
|
|
}
|
|
|
|
/**
|
|
* @brief Main function
|
|
* @param argc commandline argument count (ignored)
|
|
* @param argv commandline array of arguments (ignored)
|
|
* @returns 0 on exit
|
|
*/
|
|
|
|
|
|
int main(int argc, char const *argv[])
|
|
{
|
|
|
|
|
|
test();
|
|
|
|
return 0;
|
|
}
|