116 int iter,i,k; int k1,inc1; int k2,j,k3,k4; char *buff1,*buff2,tmp; long loc; buff1=(char *)malloc(N*sizeof(char)); buff2=(char *)malloc(N*sizeof(char)); N1=N/2; inc=1; inc1=2; 00 02 04 06 11 13 15 17 20 22 24 26 01 03 05 07 10 12 14 16 21 23 25 27 30 32 34 36 41 43 45 47 50 52 54 56 31 33 35 37 40 42 44 46 51 53 55 57 61 63 65 67 70 72 74 76 60 62 64 66 71 73 75 77 41 43 50 52 40 42 51 53 61 63 70 72 60 62 71 73 bíc 0 bíc 2 04 06 15 17 24 26 05 07 14 16 25 27 34 36 35 37 00 02 11 13 20 22 01 03 10 12 21 23 30 32 31 33 45 47 54 56 44 46 55 57 65 67 74 76 64 66 75 77 00 02 04 06 11 13 15 17 20 22 24 26 01 03 05 07 10 12 14 16 21 23 25 27 30 32 34 36 41 43 45 47 50 52 54 56 31 33 35 37 40 42 44 46 51 53 55 57 61 63 65 67 70 72 74 76 60 62 64 66 71 73 75 77 00 11 01 10 02 13 03 12 04 1505 14 06 17 07 16 20 21 30 31 22 23 32 33 24 25 34 35 26 27 36 37 41 50 40 51 43 52 42 53 45 5444 55 47 56 46 57 61 70 60 71 63 72 62 73 65 7464 75 67 76 66 77 bíc 1 Ma trËn chuyÓn vÞ 117 Hình 6.10 Thuật toán của Eklundh cho dịch chuyển một ma trận. for(iter=0;iter<n;iter++) { gotoxy(1,2); printf("iteration # %4d",iter+1); k1=0 ; for(k=0;k<N1;k++) { for(i=k1;i<(k1+inc);i++) loc=(long)(N)*(long)(i); if(fseek(fptr,loc,SEEK_SET)!=0) { perror("fseek failed"); exit(1); } else { gotoxy(1,3); printf("Reading row # %4d",i); for(k4=0;k4<N;k4++) *(buff1+k4)=fgetc(fptr); { loc=(long)(N)*(long)(i+inc); } if(fseek(fptr,loc,SEEK_SET)!=0) { perror("fseek failed"); exit(1) ; } else { gotoxy(1,4); printf("Reading row # %4d",i+inc); for(k4=0;k4<N;k4++) *(buff2+k4)=fgetc(fptr); } k3=0; for(k2=0;k2<N1;k2++) { 118 for(j=k3;j<(k3+inc);j++) { tmp=*(buff1+j+inc); *(buff1+j+inc)=*(buff2+j); *(buff2+j)=tmp; } k3+=inc1 ; } loc=(long)(N)*(long)i; if(fseek(fptr,loc,SEEK_SET)!=0) { perror("fseek failed"); exit( 1 ) ; } else { gotoxy(1,3); printf("writing row # %4d",i); for(k4=0;k4<N;k4++) putc((char)(*(buff1+k4)),fptr); } loc=(long)(N)*(long)(i+inc); if(fseek(fptr,loc,SEEK_SET)!=0) { perror("fseek failed"); exit(1) ; } else { gotoxy(1,4); printf("writing row # %4d",i+inc); for(k4=0;k4<N;k4++) putc((char)(*(buff2+k4)),fptr); } } k1+=inc1 ; } inc*=2; 119 inc1*=2; N1/=2; } Để kiểm tra chương trình 6.5 chúng ta sẽ áp dụng thuật toán này lên ảnh cho trong hình 6.11. ảnh này chứa trên đĩa đi kèm theo cuốn sách này dưới file có tên là “MOHSEN.IMG”. Chương trình 6.6 “ FFT2D.C” 2-D FFT /****************************** * Program developed by: * * M.A.Sid-Ahmed. * * ver. 1.0 1992. * * @ 1994 * ******************************/ /* 2D-FFT - Using Decimation-in-time routine.*/ #define pi 3.141592654 #include <stdio.h> #include <math.h> #include <alloc.h> #include <stdlib.h> #include <io.h> #include <conio.h> void bit_reversal(unsigned int *, int , int); void WTS(float *, float *, int, int); void FFT(float *xr, float *xi, float *, float *, int, int ) ; void transpose(FILE *, int, int); void FFT2D(FILE *, FILE *, float *, float*, unsigned int *,int,int,int); 120 Hình 6.11 Ảnh đã được dịch chuyển, "MOHSEN.IMG". void main() { int N,n2,m,k,i; unsigned int *L; float *wr , *wi; char file_name[14]; FILE *fptr,*fptro; double nsq; clrscr(); printf(" Enter name of input file-> "); scanf("%s",file_name); if((fptr=fopen(file_name,"rb"))==NULL) { printf("file %s does not exist.\n"); exit(1); } nsq=(double)filelength(fileno(fptr)); N=sqrt(nsq); m=(int)(log10((double)N)/log10((double)2.0)); k=1 ; 121 for(i=0;i<m;i++) k<<=1 ; if (k!=N) { printf("Length of file has to be multiples of 2.\n "); exit(1); } Hình 6.12 Ảnh dịch chuyển của “MOHSEN.IMG”. printf(" Enter file name for output file >"); scanf("%s",file_name); fptro=fopen(file_name,"wb+"); /* Allocating memory for bit reversal LUT. */ L=(unsigned int *)malloc(N*sizeof(unsigned int)); /* Generate Look-up table for bit reversal. */ bit_reversal(L,m,N); /* Allocating memory for twiddle factors. */ n2=(N>>1)-1; wr=(float *)malloc(n2*sizeof(float)); 122 wi=(float *)malloc(n2*sizeof(float)); /*Generating LUT for twiddle factors. */ WTS(wr,wi,N,-1); FFT2D(fptr,fptro,wr,wi,L,N,m,-1); } void FFT2D(FILE *fptr, FILE *fptro, float *wr, float *wi, unsigned int *L, int N, int m, int sign) { /* 2-D FFT Algorithm. */ /* fptr=file pointer to input file. fptro=file pointer to output file. Note: fptr, fptro should be opened in the main routine. They are closed before return to @he main routine. wr[1,wj[I input arrays for twiddle factors, calculated by calling procedure WTS. L[I look-up table for bit reversal. N input array size ( NxN words.) =2 to the power m. sign =-1 for 2-D FFT, =1 for 2-D IFFT. For FFT (sign= 1) the input data is assumed to be real. The result of the FFT has its origin shifted to (N/2,N/2).*/ int N2,i,j,k,kk; long loc,NB; float *xr,*xi,*buff; N2=N<<1; NB=sizeof(float)*N2; /* Allocating memory for FFT arrays ( real and imag.) */ xr=(float *)malloc(N*sizeof(float)); xi=(float *)malloc(N*sizeof(float)); buff=(float *)malloc(NB); . tra chương trình 6.5 chúng ta sẽ áp dụng thuật toán n y lên ảnh cho trong hình 6.11. ảnh n y chứa trên đĩa đi kèm theo cuốn sách n y dưới file có tên là “MOHSEN.IMG”. Chương trình 6.6 “. routine. They are closed before return to @he main routine. wr[1,wj[I input arrays for twiddle factors, calculated by calling procedure WTS. L[I look-up table for bit reversal. N input array size. 2 04 06 15 17 24 26 05 07 14 16 25 27 34 36 35 37 00 02 11 13 20 22 01 03 10 12 21 23 30 32 31 33 45 47 54 56 44 46 55 57 65 67 74 76 64 66 75 77 00 02 04 06 11 13 15 17 20 22 24 26 01 03 05 07 10 12 14 16 21 23 25 27 30 32 34 36 41 43 45 47 50 52 54 56 31 33 35 37 40 42 44 46 51 53 55 57 61 63 65 67 70 72 74 76 60 62 64 66 71 73 75 77 00 11 01 10 02 13 03 12 04 1505 14 06 17 07 16 20 21 30 31 22 23 32 33 24 25 34 35 26 27 36 37 41 50 40 51 43 52 42 53 45 5444 55 47 56 46 57 61 70 60 71 63 72 62 73 65 7464 75 67 76 66 77 bíc 1 Ma trËn chuyÓn vÞ 117 Hình 6.10 Thuật toán của Eklundh cho dịch chuyển một ma trận. for(iter=0;iter<n;iter++) { gotoxy(1,2); printf("iteration # %4d",iter+1);