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141 lines
3.2 KiB
141 lines
3.2 KiB
#include <stdlib.h>
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#include <stdio.h>
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#include <string.h>
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#include <ctype.h>
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#include <math.h>
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#include <complex>
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>
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#include<vector>
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using namespace std;
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#ifndef M_PI
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#define M_PI 3.14159265358979323846
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#endif
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typedef struct {
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long N;
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double b, a, beta, alpha;
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double tmin, tmax,h;
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int m;
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int sign;
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} fft_param;
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complex<double> expo(fft_param *fp,int k) {
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int sign = fp->sign;
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return exp(sign*2 * M_PI * 1i / ((double) k));
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}
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vector<complex<double>> fourierTrafo(fft_param *fp, vector<complex<double>> x) {
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long N = x.size();
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int sign=fp->sign;
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vector<complex<double>> gerPkt(N / 2);
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vector<complex<double>> ungerPkt(N / 2);
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if (N == 1) {
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return x;
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} else {
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for (int k = 0; k < N / 2; k++) {
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gerPkt[k] = x[2 * k];
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ungerPkt[k] = x[2 * k + 1];
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}
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vector<complex<double>> ftger(N / 2) = fourierTrafo(fp, gerPkt); //???????????????????????
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vector<complex<double>> ftunger(N / 2) = fourierTrafo(fp, ungerPkt); //???????????????????
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vector<complex<double>> out(N);
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for (int k = 0; k < N / 2; k++) {
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out[k] = (ftger[k] + ftunger[k] * expo(fp,k))/(double)N;
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out[k + N / 2] = (ftger[k] - ftunger[k] *expo(fp,k))/(double)N;
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}
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return out;
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}
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}
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vector<complex<double>> test(fft_param *fp){
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double h=fp->h;
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double tmin=fp->tmin;
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double tmax=fp->tmax;
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double t=tmin;
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int N=fp->N;
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vector<complex<double>> x(N);
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for(int k=0;k<N;k++){
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x(k)=sin(tmin+k*h);
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}
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vector<complex<double>> out = fourierTrafo(fp, x);
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fft_param n= *fp;
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n.sign=-1;
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vector<complex<double>> doppelout = fourierTrafo(&n, out);
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FILE *fp2 = fopen("testFFT.csv" ,'w');
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for(int k=0;k<N;k++){
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fprintf(fp2,"%f\t%f\t%f\n",x[k], doppelout[k],(tmin+k*h));
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}
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return x;
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}
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vector<complex<double>> makeS(fft_param *fp){
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double h=fp->h;
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double tmax=fp->tmax;
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double tmin=0;
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double t;
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double tl=fp->tl;
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double alpha=f->alpha;
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int N=fp->N;
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vector<complex<double>> s(N);
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for(int k=0;k<N;k++){
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t=tmin+k*h;
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s[k]=sin(2*M_PI*alpha*(t-tl));
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}
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return s;
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}
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vector<complex<double>> makeE(fft_param *fp){
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double h=fp->h;
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double tmax=fp->tmax;
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double tmin=0;
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double t;
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double beta=f->beta;
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double tl=fp->tl;
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double a=fp->a;
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double b=fp->b;
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int N=fp->N;
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vector<complex<double>> e(N);
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vector<complex<double>> s=makeS(fp);
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for(int k=0;k<N;k++){
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t=tmin+k*h;
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e[k]=b*sin(2*M_PI*beta*t)+a*rand(1)+s[k];
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}
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return e;
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}
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vector<complex<double>> aufgabe3 (fft_param *fp){
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double h=fp->h;
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double tmin=fp->tmin;
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double tmax=fp->tmax;
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double t=tmin;
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int N=fp->N;
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vector<complex<double>> e(N)=makeE;
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vector<complex<double>> s(N)=makeS(fp);
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vector<comlex<double>> Fe=fourierTrafo(fp,e);
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fft_param fps=*fp;
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fps.sign=-1;
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vector<comlex<double>> Fs=fourierTrafo(&fps,s);
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vector<comlex<double>> FFes(N);
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for(int k=0;k<N;k++){
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FFes[k]=Fe[k]*conj(Fs[k]);
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}
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vector<comlex<double>> FFFes(N)=fourierTrafo(fp, FFes);
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return FFFes;
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}
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double main(){
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fft_param fp;
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fp.N= pow(2,13);
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fp.tmin=0;
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fp.tmax = 100;
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fp.h=(fp.tmax-fp.tmin)/fp.N;
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fp.sign=1;
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test(&fp);
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}
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