学习DIP第6天
网上关于FFT的实例有很多,具体也可以参照上一篇,其实Matlab,OpenCV都可以很轻松的实现相关操作,但是对于学习其原理,还是自己操作下比较好。
二维FFT的是实现方法是先对行做FFT将结果放回该行,然后再对列做FFT结果放在该列,计算完所有的列以后,结果就是响应的二维FFT。
本次所有操作都是对基2的数据进行的操作。
二维IFFT网上很少见到,操作过程是:上述的傅里叶变换结果,先对每列做一维IFFT,结果放在该列,取复数矩阵其共轭,然后再按照每行做一维IFFT,其结果放在该行,即为最终结果。上代码:
1D.c:
//
// 1D.c
// Fourer
//
// Created by 谭升 on 14/11/25.
// Copyright (c) 谭升. All rights reserved.
//
#include "Fourer.h"
int isBase2(int size_n){
int k=size_n;
int z=0;
while (k/=2) {
z++;
}
k=z;
if(size_n!=(1<
return -1;
else
return k;
}
//复数基本运算
///
void Add_Complex(Complex * src1,Complex *src2,Complex *dst){
dst->imagin=src1->imagin+src2->imagin;
dst->real=src1->real+src2->real;
}
void Sub_Complex(Complex * src1,Complex *src2,Complex *dst){
dst->imagin=src1->imagin-src2->imagin;
dst->real=src1->real-src2->real;
}
void Multy_Complex(Complex * src1,Complex *src2,Complex *dst){
double r1=0.0,r2=0.0;
double i1=0.0,i2=0.0;
r1=src1->real;
r2=src2->real;
i1=src1->imagin;
i2=src2->imagin;
dst->imagin=r1*i2+r2*i1;
dst->real=r1*r2-i1*i2;
}
void Copy_Complex(Complex * src,Complex *dst){
dst->real=src->real;
dst->imagin=src->imagin;
}
void Show_Complex(Complex * src,int size_n){
if(size_n==1){
if(src->imagin>=0.0)
printf("%lf+%lfj ",src->real,src->imagin);
else
printf("%lf%lfj ",src->real,src->imagin);
}
else if(size_n>1){
for(int i=0;i
if(src[i].imagin>=0.0){
printf("%lf+%lfj ",src[i].real,src[i].imagin);
}
else
printf("%lf%lfj ",src[i].real,src[i].imagin);
}
}
//计算WN
///
void getWN(double n,double size_n,Complex * dst){
double x=2.0*M_PI*n/size_n;
dst->imagin=-sin(x);
dst->real=cos(x);
}
//随机初始化输入
///
void setInput(double * data,int n){
printf("Setinput signal:\n");
srand((int)time(0));
for(int i=0;i
data[i]=rand()%VALUE_MAX;
}
}
//标准DFT
///
void DFT(double * src,Complex * dst,int size){
for(int m=0;m
double real=0.0;
double imagin=0.0;
for(int n=0;n
double x=M_PI*2*m*n;
real+=src[n]*cos(x/size);
imagin+=src[n]*(-sin(x/size));
}
dst[m].imagin=imagin;
dst[m].real=real;
}
}
//IDT,复原傅里叶
///
void IDFT(Complex *src,Complex *dst,int size){
for(int m=0;m
double real=0.0;
double imagin=0.0;
for(int n=0;n
double x=M_PI*2*m*n/size;
real+=src[n].real*cos(x)-src[n].imagin*sin(x);
imagin+=src[n].real*sin(x)+src[n].imagin*cos(x);
}
real/=SIZE;
imagin/=SIZE;
if(dst!=NULL){
dst[m].real=real;
dst[m].imagin=imagin;
}
}
}
//FFT前,对输入数据重新排序
///
int FFTReal_remap(double * src,int size_n){
if(size_n==1)
return 0;
double * temp=(double *)malloc(sizeof(double)*size_n);
for(int i=0;i
if(i%2==0)
temp[i/2]=src[i];
else
temp[(size_n+i)/2]=src[i];
for(int i=0;i
src[i]=temp[i];
free(temp);
FFTReal_remap(src, size_n/2);
FFTReal_remap(src+size_n/2, size_n/2);
return 1;
}
int FFTComplex_remap(Complex * src,int size_n){
if(size_n==1)
return 0;
Complex * temp=(Complex *)malloc(sizeof(Complex)*size_n);
for(int i=0;i
if(i%2==0)
Copy_Complex(&src[i],&(temp[i/2]));
else
Copy_Complex(&(src[i]),&(temp[(size_n+i)/2]));
for(int i=0;i
Copy_Complex(&(temp[i]),&(src[i]));
free(temp);
FFTComplex_remap(src, size_n/2);
FFTComplex_remap(src+size_n/2, size_n/2);
return 1;
}
//FFT公式
///
void FFT(Complex * src,Complex * dst,int size_n){
int k=size_n;
int z=0;
while (k/=2) {
z++;
}
k=z;
if(size_n!=(1<
exit(0);
Complex * src_com=(Complex*)malloc(sizeof(Complex)*size_n);
if(src_com==NULL)
exit(0);
for(int i=0;i
Copy_Complex(&src[i], &src_com[i]);
}
FFTComplex_remap(src_com, size_n);
for(int i=0;i
z=0;
for(int j=0;j
if((j/(1<
Complex wn;
getWN(z, size_n, &wn);
Multy_Complex(&src_com[j], &wn,&src_com[j]);
z+=1<
Complex temp;
int neighbour=j-(1<
temp.real=src_com[neighbour].real;
temp.imagin=src_com[neighbour].imagin;
Add_Complex(&temp, &src_com[j], &src_com[neighbour]);
Sub_Complex(&temp, &src_com[j], &src_com[j]);
}
else
z=0;
}
}
for(int i=0;i
Copy_Complex(&src_com[i], &dst[i]);
}
free(src_com);
}
void RealFFT(double * src,Complex * dst,int size_n){
int k=size_n;
int z=0;
while (k/=2) {
z++;
}
k=z;
if(size_n!=(1<
exit(0);
Complex * src_com=(Complex*)malloc(sizeof(Complex)*size_n);
if(src_com==NULL)
exit(0);
for(int i=0;i
src_com[i].real=src[i];
src_com[i].imagin=0;
}
FFTComplex_remap(src_com, size_n);
for(int i=0;i
z=0;
for(int j=0;j
if((j/(1<
Complex wn;
getWN(z, size_n, &wn);
Multy_Complex(&src_com[j], &wn,&src_com[j]);
z+=1<
Complex temp;
int neighbour=j-(1<
temp.real=src_com[neighbour].real;
temp.imagin=src_com[neighbour].imagin;
Add_Complex(&temp, &src_com[j], &src_com[neighbour]);
Sub_Complex(&temp, &src_com[j], &src_com[j]);
}
else
z=0;
}
}
for(int i=0;i
Copy_Complex(&src_com[i], &dst[i]);
}
free(src_com);
}
//IFFT实现
void IFFT(Complex * src,Complex * dst,int size_n){
for(int i=0;i
src[i].imagin=-src[i].imagin;
FFTComplex_remap(src, size_n);
int z,k;
if((z=isBase2(size_n))!=-1)
k=isBase2(size_n);
else
exit(0);
for(int i=0;i
z=0;
for(int j=0;j
if((j/(1<
Complex wn;
getWN(z, size_n, &wn);
Multy_Complex(&src[j], &wn,&src[j]);
z+=1<
Complex temp;
int neighbour=j-(1<
Copy_Complex(&src[neighbour], &temp);
Add_Complex(&temp, &src[j], &src[neighbour]);
Sub_Complex(&temp, &src[j], &src[j]);
}
else
z=0;
}
}
for(int i=0;i
dst[i].imagin=(1./size_n)*src[i].imagin;
dst[i].real=(1./size_n)*src[i].real;
}
}
2D.c
//
// 2D.c
// Fourer
//
// Created by 谭升 on 14/11/25.
// Copyright (c) 谭升. All rights reserved.
//
#include "Fourer.h"
/*
*/
int DFT2D(double *src,Complex *dst,int size_w,int size_h){
for(int u=0;u
for(int v=0;v
double real=0.0;
double imagin=0.0;
for(int i=0;i
for(int j=0;j
double I=src[i*size_w+j];
double x=M_PI*2*((double)i*u/(double)size_w+(double)j*v/(double)size_h);
real+=cos(x)*I;
imagin+=-sin(x)*I;
}
}
dst[u*size_w+v].real=real;
dst[u*size_w+v].imagin=imagin;
}
}
return 0;
}
/*
*/
int IDFT2D(Complex *src,Complex *dst,int size_w,int size_h){
for(int i=0;i
for(int j=0;j
double real=0.0;
double imagin=0.0;
for(int u=0;u
for(int v=0;v
double R=src[u*size_w+v].real;
double I=src[u*size_w+v].imagin;
double x=M_PI*2*((double)i*u/(double)size_w+(double)j*v/(double)size_h);
real+=R*cos(x)-I*sin(x);
imagin+=I*cos(x)+R*sin(x);
}
}
dst[i*size_w+j].real=(1./(size_w*size_h))*real;
dst[i*size_w+j].imagin=(1./(size_w*size_h))*imagin;
}
}
return 0;
}
/*
*/
void ColumnVector(Complex * src,Complex * dst,int size_w,int size_h){
for(int i=0;i
Copy_Complex(&src[size_w*i], &dst[i]);
}
/*
*/
void IColumnVector(Complex * src,Complex * dst,int size_w,int size_h){
for(int i=0;i
Copy_Complex(&src[i],&dst[size_w*i]);
}
/*
*/
int FFT2D(double *src,Complex *dst,int size_w,int size_h){
if(isBase2(size_w)==-1||isBase2(size_h)==-1)
exit(0);
Complex *temp=(Complex *)malloc(sizeof(Complex)*size_h*size_w);
if(temp==NULL)
return -1;
for(int i=0;i
RealFFT(&src[size_w*i], &temp[size_w*i], size_w);
}
Complex *Column=(Complex *)malloc(sizeof(Complex)*size_h);
if(Column==NULL)
return -1;
for(int i=0;i
ColumnVector(&temp[i], Column, size_w, size_h);
FFT(Column, Column, size_h);
IColumnVector(Column, &temp[i], size_w, size_h);
}
for(int i=0;i
Copy_Complex(&temp[i], &dst[i]);
free(temp);
free(Column);
return 0;
}
/*
*/
int IFFT2D(Complex *src,Complex *dst,int size_w,int size_h){
if(isBase2(size_w)==-1||isBase2(size_h)==-1)
exit(0);
Complex *temp=(Complex *)malloc(sizeof(Complex)*size_h*size_w);
if(temp==NULL)
return -1;
Complex *Column=(Complex *)malloc(sizeof(Complex)*size_h);
if(Column==NULL)
return -1;
for(int i=0;i
ColumnVector(&src[i], Column, size_w, size_h);
IFFT(Column, Column, size_h);
IColumnVector(Column, &src[i], size_w, size_h);
}
for(int i=0;i
src[i].imagin=-src[i].imagin;
for(int i=0;i
IFFT(&src[size_w*i], &temp[size_w*i], size_w);
}
for(int i=0;i
Copy_Complex(&temp[i], &dst[i]);
free(temp);
free(Column);
return 0;
}
结果: