{"id":66,"date":"2020-12-19T11:25:36","date_gmt":"2020-12-19T03:25:36","guid":{"rendered":"https:\/\/www.one-year.cn\/?p=66"},"modified":"2022-02-28T09:31:27","modified_gmt":"2022-02-28T01:31:27","slug":"%e7%94%a8c%e8%af%ad%e8%a8%80%e5%ae%9e%e7%8e%b0dit-fft%e5%92%8cdif-fft","status":"publish","type":"post","link":"https:\/\/www.constantinefun.com\/?p=66","title":{"rendered":"\u7528C\u8bed\u8a00\u5b9e\u73b0dit-fft\u548cdif-fft"},"content":{"rendered":"\n
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\u5173\u4e8eFFT<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n
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\u5b9e\u73b0\u65b9\u6cd5<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n
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\u5b8c\u6574\u4ee3\u7801<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

\u603b\u8ff0<\/strong>\uff1a<\/h2>\n\n\n\n

\u901a\u8fc7C\u8bed\u8a00\u5b9e\u73b0\u5148\u5c0611\u4f4d\u5e8f\u5217\u8fdb\u884c\u5ef6\u62d3\u52301024\u4f4d\u540e\u8fdb\u884cfft\u548cifft\u53d8\u6362\uff08\u8981\u6c42\u7528dit-fft\u548cdif-fft\u5206\u522b\u5b9e\u73b0\uff09\u3002<\/p>\n\n\n\n

\u4e00\u3001\u5173\u4e8eFFT<\/h2>\n\n\n\n
  • FFT\u7b80\u4ecb\uff1a<\/li><\/ul>\n\n\n\n

    FFT\u662f\u4e00\u79cdDFT\u7684\u9ad8\u6548\u7b97\u6cd5\uff0c\u79f0\u4e3a\u5feb\u901f\u5085\u7acb\u53f6\u53d8\u6362\uff08fast Fourier transform\uff09\u3002\u5085\u91cc\u53f6\u53d8\u6362\u662f\u65f6\u57df\u4e00\u9891\u57df\u53d8\u6362\u5206\u6790\u4e2d\u6700\u57fa\u672c\u7684\u65b9\u6cd5\u4e4b\u4e00\u3002\u5728\u6570\u5b57\u5904\u7406\u9886\u57df\u5e94\u7528\u7684\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362(DFT\uff1aDiscrete Fourier Transform)\u662f\u8bb8\u591a\u6570\u5b57\u4fe1\u53f7\u5904\u7406\u65b9\u6cd5\u7684\u57fa\u7840 \u3002<\/p>\n\n\n\n

    • \u57fa\u672c\u539f\u7406\uff1a<\/li><\/ul>\n\n\n\n

      FFT\u7b97\u6cd5\u662f\u628a\u957f\u5e8f\u5217\u7684DFT\u9010\u6b21\u5206\u89e3\u4e3a\u8f83\u77ed\u5e8f\u5217\u7684DFT\u3002
      \u6309\u7167\u62bd\u53d6\u65b9\u5f0f\u7684\u4e0d\u540c\u53ef\u5206\u4e3aDIT-FFT(\u6309\u65f6\u95f4\u62bd\u53d6)\u548cDIF-FFT(\u6309\u9891\u7387\u62bd\u53d6)\u7b97\u6cd5\u3002\u6309\u8776\u5f62\u8fd0\u7b97\u7684\u6784\u6210\u4e0d\u540c\u53ef\u5206\u4e3a\u57fa2\uff0c\u57fa4\uff0c\u57fa8\uff0c\u4ee5\u53ca\u4efb\u610f\u56e0\u5b50\u7684\u7c7b\u578b\u3002<\/p>\n\n\n\n

      • \u8fed\u4ee3\u5173\u7cfb\uff1a<\/li><\/ul>\n\n\n\n
        \"\"\/<\/div><\/figure>\n\n\n\n

        \u4e8c\u3001\u5b9e\u73b0\u65b9\u6cd5<\/h2>\n\n\n\n
        • \u56e0\u4e3a\u9700\u8981\u8fdb\u884c\u590d\u6570\u8fd0\u7b97\uff0c\u56e0\u6b64\u5b9a\u4e49\u590d\u6570\u7ed3\u6784\u4f53\u548c\u76f8\u5173\u8fd0\u7b97<\/li><\/ul>\n\n\n\n
          \/\/\u590d\u6570\u7ed3\u6784\u4f53\n<\/em>struct compx\n{\n    double real;\n    double imag;\n} compx ;\n\/\/\u4e24\u590d\u6570\u76f8\u4e58\n<\/em>struct compx EE(struct compx b1, struct compx b2)\n{\n    struct compx b3;\n    b3.real = b1.real * b2.real - b1.imag * b2.imag;\n    b3.imag = b1.real * b2.imag + b1.imag * b2.real;\n    return(b3);\n}\n\/\/\u5bf9\u6570\u8ba1\u7b97\u51fd\u6570\n<\/em>uint <\/strong>Log(uchar <\/strong>BaseNumber,uint <\/strong>AntiNumber)\n{\n    uint <\/strong>m=0;\n    while(1)\n    {\n        AntiNumber=AntiNumber\/BaseNumber;\n        if(AntiNumber)m++;\n        else break;\n    }\n    return m;\n}<\/code><\/pre>\n\n\n\n
          • DIT-FFT(\u6309\u65f6\u95f4\u62bd\u53d6)<\/li><\/ul>\n\n\n\n
            1. \u8fdb\u884c\u7801\u4f4d\u5012\u7f6e<\/li>
            2. \u518d\u901a\u8fc7\u8776\u5f62\u8fd0\u7b97<\/li><\/ol>\n\n\n\n
              \/\/DIT-FFT\u51fd\u6570\nvoid FFT_DIT(struct compx *xin, int N)\n{\n    int f, m, LH, nm, i, k, j, L;\n    double p , ps ;\n    int le,B, ip;\n    double pi;\n    struct compx w, t;\n    LH=N \/ 2;\n    f=N;\n    for(m = 1;(f = f \/ 2) != 1; m++){;}    \/\/2\u7684m\u6b21\u65b9=N\uff0cm\u4e3a\u7ea7\u6570\n    nm = N - 2;\n    j = N \/ 2;\n    \/*\u53d8\u5740\u8fd0\u7b97*\/\n    for(i = 1;i <= nm; i++)\n    {\n        if(i < j)\n        {\n            t = xin[j];\n            xin[j] = xin[i];\n            xin[i] = t;\n        }\n        k = LH;\n        while(j >= k)\n        {\n            j = j - k;\n            k = k \/ 2;\n        }\n        j = j + k;\n    }\n    \/*fft_dit\u8fd0\u7b97*\/\n    for(L = 0; L <= m - 1; L++)    \/\/\u6bcf\u4e00\u7ea7\n    {\n        le =(int) pow(2.0, L + 1);\/\/\u5177\u6709\u76f8\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u8776\u5f62\u8fd0\u7b97\u7684\u95f4\u9694\n        B = le \/ 2; \/\/2\u7684L\u6b21\u65b9\uff0c\u4e0d\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u4e2a\u6570\uff0c\u8776\u5f62\u8fd0\u7b97\u4e24\u652f\u95f4\u9694\n        pi=3.141592653589793;\n        for(j = 0;j <= B - 1; j++)\n        {\n            p = pow(2.0, m - L - 1) * j;\n            ps = 2 * pi \/ N * p;\/\/\u65cb\u8f6c\u56e0\u5b50\n            w.real = cos(ps);\n            w.imag = -sin(ps);\n            for(i = j; i <= N - 1; i = i + le)\n            {\n                ip = i + B;\n                t = EE(xin[ip], w);\n                xin[ip].real = xin[i].real - t.real;\n                xin[ip].imag = xin[i].imag - t.imag;\n                xin[i].real = xin[i].real + t.real;\n                xin[i].imag = xin[i].imag + t.imag;\n            }\n        }\n    }\n    return ;\n}<\/code><\/pre>\n\n\n\n
              • DIF-FFT(\u6309\u9891\u7387\u62bd\u53d6)<\/li><\/ul>\n\n\n\n
                \n
                1. \u5148\u8fdb\u884c\u5bf9\u5e94\u7684\u8776\u5f62\u8fd0\u7b97<\/li>
                2. \u518d\u8fdb\u884c\u7801\u4f4d\u5012\u7f6e<\/li><\/ol>\n\n\n\n
                  \n
                  \/\/DIF-FFT<\/em>\u51fd\u6570
                  <\/em>void FFT_DIF(struct compx *xin, int N)
                  {
                      int f, m, LH, nm, i, k, j, L;
                      double p, ps ;
                      int le, B, ip;
                      double pi;
                      struct compx w, t;
                      LH = N \/ 2;
                      f = N;
                      for(m = 1; (f = f \/ 2) != 1; m++){;}\/\/2<\/em>\u7684<\/em>m<\/em>\u6b21\u65b9<\/em>=N<\/em>\uff0c<\/em>m<\/em>\u4e3a\u7ea7\u6570
                  <\/em>    <\/em>\/*fft_dif<\/em>\u8fd0\u7b97<\/em>*\/
                  <\/em>    <\/em>for(L = 0; L <= m - 1; L++)    \/\/<\/em>\u6bcf\u4e00\u7ea7
                  <\/em>    <\/em>{
                          le =(int) pow(2.0, m - L);\/\/<\/em>\u5177\u6709\u76f8\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u8776\u5f62\u8fd0\u7b97\u7684\u95f4\u9694
                  <\/em>        <\/em>B = le \/ 2; \/\/2<\/em>\u7684<\/em>m - L - 1<\/em>\u6b21\u65b9\uff0c\u4e0d\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u4e2a\u6570\uff0c\u8776\u5f62\u8fd0\u7b97\u4e24\u652f\u95f4\u9694
                  <\/em>        <\/em>pi = 3.141592653589793;
                          for(j = 0; j <= B - 1; j++)
                          {
                              p = pow(2.0, L) * j;
                              ps = 2 * pi \/ N * p;\/\/<\/em>\u65cb\u8f6c\u56e0\u5b50
                  <\/em>            <\/em>w.real = cos(ps);
                              w.imag = -sin(ps);
                              for(i = j; i <= N-1; i = i + le)
                              {
                                  ip = i + B;
                                  t = xin[i];
                                  xin[i].real = t.real + xin[ip].real;
                                  xin[i].imag = t.imag + xin[ip].imag;
                                  xin[ip].real = t.real - xin[ip].real;
                                  xin[ip].imag = t.imag - xin[ip].imag;
                                  xin[ip] = EE(xin[ip], w);
                              }
                          }
                      }
                      nm = N - 2;
                      j = N \/ 2;
                      \/*<\/em>\u53d8\u5740\u8fd0\u7b97<\/em>*\/
                  <\/em>    <\/em>for(i = 1; i <= nm; i++)
                      {
                          if(i < j){t = xin[j]; xin[j] = xin[i]; xin[i] = t;}
                          k = LH;
                          while(j >= k){j = j - k; k = k \/ 2;}
                          j = j + k;
                      }
                      return ;
                  }<\/code><\/pre>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
                  \n
                  • \u4e3b\u7a0b\u5e8f<\/li><\/ul>\n\n\n\n
                    int main()\n{\n    char method,start;\t\/\/ fft and ifft method\n    uint y[12]={1,2,3,4,5,6,7,8,9,0,0}; \/\/\u8f93\u5165\u5e8f\u5217\n    int i,j,k;\n    FILE *fp;\n    fp = fopen(\"fft_out.txt\",\"w\");;\n    printf(\"\u521d\u59cb\u5e8f\u5217:\\n\");\n    fprintf(fp,\"\u521d\u59cb\u5e8f\u5217:\\n\");\n    for(i=0;i<94;i++)\/\/\u957f\u5ea6\u4e3aMAX\u7684\u624b\u673a\u53f7\n    {\n        for(j=0,k=0;j<11;j++,k=j+i*11)\n        {\n            if (k == MAX){break;}\n            s[k].imag=0;\n            s[k].real=y[j];\n            printf(\"%.4f + %.4fi\\n\",s[k].real,s[k].imag);\n            fprintf(fp,\"%.4f + %.4fi\\n\",s[k].real,s[k].imag);\n        }\n    }\n}<\/code><\/pre>\n<\/div><\/div>\n\n\n\n
                    \u4e09\u3001\u5b8c\u6574\u7a0b\u5e8f\u4ee3\u7801\uff1a<\/h2>\n\n\n\n
                    \/\/\u5934\u6587\u4ef6\u5f15\u7528\n#include <math.h>\n#include <stdio.h>\n#include <stdlib.h>\n\n\n\/\/\u5168\u5c40\u5b8f\u5b9a\u4e49\n#define uint unsigned int\n#define uchar unsigned char\n#define MAX 1024 \/\/\u5b9a\u4e49\u5e8f\u5217\u957f\u5ea6\n\n\n\/\/\u590d\u6570\u7ed3\u6784\u4f53\nstruct compx\n{\n    double real;\n    double imag;\n} compx ;\n\n\n\/\/\u4e24\u590d\u6570\u76f8\u4e58\nstruct compx EE(struct compx b1, struct compx b2)\n{\n    struct compx b3;\n    b3.real = b1.real * b2.real - b1.imag * b2.imag;\n    b3.imag = b1.real * b2.imag + b1.imag * b2.real;\n    return(b3);\n}\n\n\n\/\/\u5168\u5c40\u53d8\u91cf\u5b9a\u4e49\nuint   Num = 1024;\ndouble result[MAX];\nstruct  compx s[MAX];\nconst double pp = 3.141592653589793 ;\n\n\n\/\/\u5bf9\u6570\u8ba1\u7b97\u51fd\u6570\nuint Log(uchar BaseNumber,uint AntiNumber)\n{\n    uint m=0;\n    while(1)\n    {\n        AntiNumber=AntiNumber\/BaseNumber;\n        if(AntiNumber)m++;\n        else break;\n    }\n    return m;\n}\n\n\n\/\/DIT-FFT\u51fd\u6570\nvoid FFT_DIT(struct compx *xin, int N)\n{\n    int f, m, LH, nm, i, k, j, L;\n    double p , ps ;\n    int le,B, ip;\n    double pi;\n    struct compx w, t;\n    LH=N \/ 2;\n    f=N;\n    for(m = 1;(f = f \/ 2) != 1; m++){;}\t\/\/2\u7684m\u6b21\u65b9=N\uff0cm\u4e3a\u7ea7\u6570\n    nm = N - 2;\n    j = N \/ 2;\n    \/*\u53d8\u5740\u8fd0\u7b97*\/\n    for(i = 1;i <= nm; i++)\n    {\n        if(i < j)\n        {\n            t = xin[j];\n            xin[j] = xin[i];\n            xin[i] = t;\n        }\n        k = LH;\n        while(j >= k)\n        {\n            j = j - k;\n            k = k \/ 2;\n        }\n        j = j + k;\n    }\n    \/*fft_dit\u8fd0\u7b97*\/\n    for(L = 0; L <= m - 1; L++)\t\/\/\u6bcf\u4e00\u7ea7\n    {\n        le =(int) pow(2.0, L + 1);\/\/\u5177\u6709\u76f8\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u8776\u5f62\u8fd0\u7b97\u7684\u95f4\u9694\n        B = le \/ 2; \/\/2\u7684L\u6b21\u65b9\uff0c\u4e0d\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u4e2a\u6570\uff0c\u8776\u5f62\u8fd0\u7b97\u4e24\u652f\u95f4\u9694\n        pi=3.141592653589793;\n        for(j = 0;j <= B - 1; j++)\n        {\n            p = pow(2.0, m - L - 1) * j;\n            ps = 2 * pi \/ N * p;\/\/\u65cb\u8f6c\u56e0\u5b50\n            w.real = cos(ps);\n            w.imag = -sin(ps);\n            for(i = j; i <= N - 1; i = i + le)\n            {\n                ip = i + B;\n                t = EE(xin[ip], w);\n                xin[ip].real = xin[i].real - t.real;\n                xin[ip].imag = xin[i].imag - t.imag;\n                xin[i].real = xin[i].real + t.real;\n                xin[i].imag = xin[i].imag + t.imag;\n            }\n        }\n    }\n    return ;\n}\n\n\n\/\/DIF-FFT\u51fd\u6570\nvoid FFT_DIF(struct compx *xin, int N)\n{\n    int f, m, LH, nm, i, k, j, L;\n    double p, ps ;\n    int le, B, ip;\n    double pi;\n    struct compx w, t;\n    LH = N \/ 2;\n    f = N;\n    for(m = 1; (f = f \/ 2) != 1; m++){;}\/\/2\u7684m\u6b21\u65b9=N\uff0cm\u4e3a\u7ea7\u6570\n    \/*fft_dif\u8fd0\u7b97*\/\n    for(L = 0; L <= m - 1; L++)\t\/\/\u6bcf\u4e00\u7ea7\n    {\n        le =(int) pow(2.0, m - L);\/\/\u5177\u6709\u76f8\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u8776\u5f62\u8fd0\u7b97\u7684\u95f4\u9694\n        B = le \/ 2; \/\/2\u7684m - L - 1\u6b21\u65b9\uff0c\u4e0d\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u4e2a\u6570\uff0c\u8776\u5f62\u8fd0\u7b97\u4e24\u652f\u95f4\u9694\n        pi = 3.141592653589793;\n        for(j = 0; j <= B - 1; j++)\n        {\n            p = pow(2.0, L) * j;\n            ps = 2 * pi \/ N * p;\/\/\u65cb\u8f6c\u56e0\u5b50\n            w.real = cos(ps);\n            w.imag = -sin(ps);\n            for(i = j; i <= N-1; i = i + le)\n            {\n                ip = i + B;\n                t = xin[i];\n                xin[i].real = t.real + xin[ip].real;\n                xin[i].imag = t.imag + xin[ip].imag;\n                xin[ip].real = t.real - xin[ip].real;\n                xin[ip].imag = t.imag - xin[ip].imag;\n                xin[ip] = EE(xin[ip], w);\n            }\n        }\n    }\n    nm = N - 2;\n    j = N \/ 2;\n    \/*\u53d8\u5740\u8fd0\u7b97*\/\n    for(i = 1; i <= nm; i++)\n    {\n        if(i < j){t = xin[j]; xin[j] = xin[i]; xin[i] = t;}\n        k = LH;\n        while(j >= k){j = j - k; k = k \/ 2;}\n        j = j + k;\n    }\n    return ;\n}\n\n\n\/\/IFFT1\u51fd\u6570\nvoid IFFT_DIT(struct compx *xin, int N)\n{\n    int f, m, LH, nm, i, k, j, L;\n    double p, ps ;\n    int le, B, ip;\n    double pi;\n    struct compx w, t;\n    LH = N \/ 2;\n    f=N;\n    for(m = 1; (f = f \/ 2) != 1; m++){;}\/\/2\u7684m\u6b21\u65b9=N\uff0cm\u4e3a\u7ea7\u6570\n    \/*fft_dif\u8fd0\u7b97*\/\n    for(L = 0; L <= m - 1; L++)\t\/\/\u6bcf\u4e00\u7ea7\n    {\n        le = (int) pow(2.0, m - L);\/\/\u5177\u6709\u76f8\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u8776\u5f62\u8fd0\u7b97\u7684\u95f4\u9694\n        B = le \/ 2; \/\/2\u7684m - L - 1\u6b21\u65b9\uff0c\u4e0d\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u4e2a\u6570\uff0c\u8776\u5f62\u8fd0\u7b97\u4e24\u652f\u95f4\u9694\n        pi=3.141592653589793 ;\n        for(j = 0; j <= B-1; j++)\n        {\n            p = pow(2.0, L) * j;\n            ps = -2 * pi \/ N * p;\/\/\u65cb\u8f6c\u56e0\u5b50\n            w.real = cos(ps);\n            w.imag = -sin(ps);\n            for(i = j; i <= N - 1; i = i + le)\n            {\n                ip = i + B;\n                t = xin[i];\n                xin[i].real = (t.real + xin[ip].real) * 0.5;\n                xin[i].imag = (t.imag + xin[ip].imag) * 0.5;\n                xin[ip].real = (t.real - xin[ip].real) * 0.5;\n                xin[ip].imag = (t.imag - xin[ip].imag) * 0.5;\n                xin[ip] = EE(xin[ip], w);\n            }\n        }\n    }\n    nm = N - 2;\n    j = N \/ 2;\n    \/*\u53d8\u5740\u8fd0\u7b97*\/\n    for(i = 1; i <= nm; i++)\n    {\n        if(i < j){t = xin[j]; xin[j]=xin[i]; xin[i]=t;}\n        k = LH;\n        while(j >= k){j = j - k; k = k \/ 2;}\n        j = j + k;\n    }\n    return ;\n}\n\n\n\/\/IFFT2\u51fd\u6570\nvoid IFFT_DIF(struct compx *xin, int N)\n{\n    int f, m, LH, nm, i, k, j, L;\n    double p, ps ;\n    int le, B, ip;\n    double pi;\n    struct compx w, t;\n    LH = N \/ 2;\n    f = N;\n    for(m = 1; (f = f \/ 2) != 1; m++){;}\/\/2\u7684m\u6b21\u65b9=N\uff0cm\u4e3a\u7ea7\u6570\n    nm = N - 2;\n    j = N \/ 2;\n    \/*\u53d8\u5740\u8fd0\u7b97*\/\n    for(i = 1; i <= nm; i++)\n    {\n        if(i < j){t = xin[j]; xin[j] = xin[i]; xin[i] = t;}\n        k = LH;\n        while(j>=k)\n        {\n            j = j - k;\n            k = k \/ 2;\n        }\n        j = j + k;\n    }\n    \/*fft_dit\u8fd0\u7b97*\/\n    for(L = 0; L <=m - 1; L++)\t\/\/\u6bcf\u4e00\u7ea7\n    {\n        le=(int) pow(2.0, L + 1);\/\/\u5177\u6709\u76f8\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u8776\u5f62\u8fd0\u7b97\u7684\u95f4\u9694\n        B = le \/ 2; \/\/2\u7684L\u6b21\u65b9\uff0c\u4e0d\u540c\u65cb\u8f6c\u56e0\u5b50\u7684\u4e2a\u6570\uff0c\u8776\u5f62\u8fd0\u7b97\u4e24\u652f\u95f4\u9694\n        pi=3.141592653589793 ;\n        for(j = 0; j <= B - 1; j++)\n        {\n            p = pow(2.0, m - L - 1) * j;\n            ps = -2 * pi \/ N * p;\/\/\u65cb\u8f6c\u56e0\u5b50\n            w.real = cos(ps);\n            w.imag = -sin(ps);\n            for(i = j; i <= N - 1; i = i + le)\n            {\n                ip = i + B;\n                t = EE(xin[ip], w);\n                xin[ip].real = (xin[i].real-t.real) * 0.5;\n                xin[ip].imag = (xin[i].imag-t.imag) * 0.5;\n                xin[i].real = (xin[i].real+t.real) * 0.5;\n                xin[i].imag = (xin[i].imag+t.imag) * 0.5;\n            }\n        }\n    }\n    return ;\n}\n\n\/\/\u4e3b\u51fd\u6570\nint main()\n{\n    char method,start;\t\/\/ fft and ifft method\n    uint y[12]={1,2,3,4,5,6,7,8,9,0,0}; \/\/\u8f93\u5165\u5e8f\u5217\n    int i,j,k;\n    FILE *fp;\n    fp = fopen(\"fft_out.txt\",\"w\");;\n    printf(\"\u521d\u59cb\u5e8f\u5217:\\n\");\n    fprintf(fp,\"\u521d\u59cb\u5e8f\u5217:\\n\");\n    for(i=0;i<94;i++)\/\/\u957f\u5ea6\u4e3aMAX\u7684\u624b\u673a\u53f7\n    {\n        for(j=0,k=0;j<11;j++,k=j+i*11)\n        {\n            if (k == MAX)\n            {\n                break;\n            }\n            s[k].imag=0;\n            s[k].real=y[j];\n            printf(\"%.4f + %.4fi\\n\",s[k].real,s[k].imag);\n            fprintf(fp,\"%.4f + %.4fi\\n\",s[k].real,s[k].imag);\n        }\n    }\n    while(1)\n    {\n        printf(\"Input the fft decimation method(T or t for dit, F or f for dif): \");\n        method = getchar();\n        if (method == 'T' || method == 't')\n        {\n            FFT_DIT(s, Num);\n            printf(\"\\ndit-fft results:\\n\");\n            fprintf(fp,\"\\ndit-fft results:\\n\");\n            for(i = 0; i  < Num; i++)\n            {\n                printf(\"%.4f\", s[i].real);\n                printf(\"+j(%.4f)\\n\", s[i].imag);\n                fprintf(fp,\"%.4f +j(%.4f)\\n\",s[i].real,s[i].imag);\n            }\n            IFFT_DIT(s, Num);\n            printf(\"\\nifft0 results:\\n\");\n            fprintf(fp,\"\\nifft0 results:\\n\");\n            for(i = 0; i < Num; i++)\n            {\n                if(i % 11 != 0)\n                {\n                    printf(\"%.4f\", s[i].real);\n                    printf(\"+j(%.4f)\\n\", s[i].imag);\n                    fprintf(fp,\"%.4f +j(%.4f)\\n\",s[i].real,s[i].imag);\n                }\n                if(i % 11 == 0)\n                {\n                    printf(\"%.4f\", s[0].real);\n                    printf(\"+j(%.4f)\\n\", s[0].imag);\n                    fprintf(fp,\"%.4f +j(%.4f)\\n\",s[0].real,s[0].imag);\n                }\n            }\n            break;\n        }\n\n        else if (method == 'F' || method == 'f')\n        {\n            FFT_DIF(s, Num);\n            printf(\"\\ndif-fft results:\\n\");\n            fprintf(fp,\"\\ndif-fft results:\\n\");\n            for(i = 0; i  < Num; i++)\n            {\n                printf(\"%.4f\", s[i].real);\n                printf(\"+j(%.4f)\\n\", s[i].imag);\n                fprintf(fp,\"%.4f +j(%.4f)\\n\",s[i].real,s[i].imag);\n            }\n            IFFT_DIF(s, Num);\n            printf(\"\\nifft1 results:\\n\");\n            fprintf(fp,\"\\nifft1 results:\\n\");\n            for(i = 0; i < Num; i++)\n            {\n                if(i % 11 != 0)\n                {\n                    printf(\"%.4f\", s[i].real);\n                    printf(\"+j(%.4f)\\n\", s[i].imag);\n                    fprintf(fp,\"%.4f +j(%.4f)\\n\",s[i].real,s[i].imag);\n                }\n                if(i % 11 == 0)\n                {\n                    printf(\"%.4f\", s[0].real);\n                    printf(\"+j(%.4f)\\n\", s[0].imag);\n                    fprintf(fp,\"%.4f +j(%.4f)\\n\",s[0].real,s[0].imag);\n                }\n            }\n            break;\n        }\n        else\n        {\n            printf(\"INPUT ERROR!\\n\");\n        }\n    }\n    FFT_DIF(s, Num);\n    printf(\"\\nfft results:\\n\");\n    fprintf(fp,\"\\nfft results:\\n\");\n    for(i = 0; i  < Num; i++)\n    {\n        printf(\"%.4f\", s[i].real);\n        printf(\"+j(%.4f)\\n\", s[i].imag);\n        fprintf(fp,\"%.4f +j(%.4f)\\n\",s[i].real,s[i].imag);\n    }\n    IFFT_DIF(s, Num);\n    printf(\"\\nifft2 results:\\n\");\n    fprintf(fp,\"\\nifft2 results:\\n\");\n    for(i = 0; i < Num; i++)\n    {\n        if(i % 11 != 0)\n        {\n            printf(\"%.4f\", s[i].real);\n            printf(\"+j(%.4f)\\n\", s[i].imag);\n            fprintf(fp,\"%.4f +j(%.4f)\\n\",s[i].real,s[i].imag);\n        }\n        if(i % 11 == 0)\n        {\n            printf(\"%.4f\", s[0].real);\n            printf(\"+j(%.4f)\\n\", s[0].imag);\n            fprintf(fp,\"%.4f +j(%.4f)\\n\",s[0].real,s[0].imag);\n        }\n    }\n    return 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
                    \u603b\u8ff0\uff1a \u901a\u8fc7C\u8bed\u8a00\u5b9e\u73b0\u5148\u5c0611\u4f4d\u5e8f\u5217\u8fdb\u884c\u5ef6\u62d3\u52301024\u4f4d\u540e\u8fdb\u884cfft\u548cifft\u53d8\u6362\uff08\u8981\u6c42\u7528dit-fft\u548cdi […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16,6,5,13],"tags":[32],"class_list":["post-66","post","type-post","status-publish","format-standard","hentry","category-c-cpp","category-dsp","category-5","category-13","tag-cdit-fftdif-fft"],"_links":{"self":[{"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=\/wp\/v2\/posts\/66","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=66"}],"version-history":[{"count":7,"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=\/wp\/v2\/posts\/66\/revisions"}],"predecessor-version":[{"id":427,"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=\/wp\/v2\/posts\/66\/revisions\/427"}],"wp:attachment":[{"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=66"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=66"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.constantinefun.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=66"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}