FFT iOS值翻倍？

Question

嗨，我正在iOS平台上的模擬器中運行fft函數

像這樣

-(Matrix*) spectralDensityWithVec:(Matrix*) vector {

    NSLog(@"Vector:%@",vector);
    int sampleSize = [vector rows];

    double *r  = [vector array]; // arc will handle the memory

    float * f = (float*) malloc(sampleSize * sizeof(float));

    for (int i = 0;i< sampleSize;i++) {
        f[i] = r[i];
    }

    // Working with 128 samples which is 2^7
    // 7
    vDSP_Length log2n = log2([self nextPowerOf2WithNumber:sampleSize]);

    FFTSetup fftSetup = vDSP_create_fftsetup(log2n,FFT_RADIX2);

    int nOver2 = sampleSize/2;

    COMPLEX_SPLIT A;

    A.realp = (float *) malloc(nOver2*sizeof(float));
    A.imagp = (float *) malloc(nOver2*sizeof(float));

    vDSP_ctoz((COMPLEX*)f, 2, &A, 1, nOver2);

    vDSP_fft_zrip(fftSetup, &A,1 ,log2n, FFT_FORWARD);

    Matrix* PSD = [Matrix matrixOfRows:sampleSize/2 Columns:1];

    Matrix* fftResult = [Matrix matrixOfRows:sampleSize Columns:1];

    // obtain the imaginary / real parts
    for (int i = 0;i < sampleSize/2;i++) {
        float realp = A.realp[i];
        float imagp = A.imagp[i];

        NSLog(@"real:%g img:%g",realp,imagp);

        float val = sqrtf((realp * realp) + (imagp * imagp)) * 2.0f /(float)sampleSize ;

        [PSD setValue:val Row:i Column:0];
        [fftResult setValue:realp Row:i Column:0];
        [fftResult setValue:imagp Row:i*2+1 Column:0];
    }

    NSLog(@"FFT Result KW Energy: %@",fftResult);

    vDSP_destroy_fftsetup(fftSetup);

    // release memory
    if (f) {
       free(f);
        f = NULL;
    }
    if (A.realp) {
        free(A.realp);
        A.realp = NULL;
    }
    if (A.imagp) {
        free(A.imagp);
        A.imagp = NULL;
    }

    return PSD;
}

有了這個向量，我得到的結果

[1.012817,
    1.022833,
    1.022028,
    1.017877,
    1.023680,
    1.016974,
    1.017746,
    1.019263,
    1.016417,
    1.020745,
    1.018643,
    1.019521,
    1.020260,
    1.018041,
    1.020829,
    1.018644,
    1.019398,
    1.020399,
    1.019222,
    1.022093,
    1.020433,
    1.020534,
    1.021503,
    1.019931,
    1.020480,
    1.018945,
    1.019238,
    1.019989,
    1.018917,
    1.019762,
    1.019021,
    1.017887,
    1.018136,
    1.019543,
    1.020242,
    1.018757,
    1.019534,
    1.019862,
    1.019060,
    1.020717,
    1.021055,
    1.020178,
    1.018108,
    1.014776,
    1.015374,
    1.018429,
    1.019895,
    1.018647,
    1.016387,
    1.017053,
    1.019572,
    1.021097,
    1.019488,
    1.017218,
    1.019876,
    1.022022,
    1.020574,
    1.021588,
    1.022298,
    1.019369,
    1.016980,
    1.016774,
    1.016079,
    1.015292]

上面向量的結果：

   130.456100
-0.017152
-0.013957
-0.020526
-0.043666
-0.003648
-0.018351
-0.006409
-0.000965
-0.015068
-0.001338
0.011731
-0.042658
-0.012478
0.018228
-0.006718
-0.026859
-0.013061
-0.019885
-0.003351
-0.005669
-0.002971
-0.023977
-0.019806
-0.036644
-0.055367
-0.015106
0.000406
-0.002309
-0.002857
-0.002926
-0.002933
0.000000
-0.005997
0.000000
-0.013211
0.000000
-0.030161
0.000000
-0.021531
0.000000
-0.028181
0.000000
-0.011275
0.000000
-0.009881
0.000000
-0.009062
0.000000
-0.010197
0.000000
0.003035
0.000000
0.038075
0.000000
0.016340
0.000000
0.008624
0.000000
0.005861
0.000000
0.003673
0.000000
0.001765

我如何與numpy fft取得此結果：

   [65.22805000000001, 
0.0, 
-0.0085759487914117867,
 -0.015603049865923341,
 -0.0069788925854868157,
 0.015041138788651551,
 -0.010263059930525575,
 0.012321275391622862,
 -0.021832981634872219,
 -0.026161796455543486,
 -0.0018237156004342254,
 -0.013884928458450145,
 -0.0091755911990841002,
 -0.016388522893239089,
 -0.003204667797210365,
 -0.033305086561749964,
 -0.00048255506211134121,
 -0.015783138731002323,
 -0.0075337096722261337,
 -0.0071538868820418761, 
-0.00066829905037151319,
 -0.017467879005406146,
 0.0058655519004814438, 
0.011289870623693908, 
-0.021329700649694319,
 0.0018507094402767038,
 -0.0062391410740094827,
 -0.013248826390988894, 
0.0091139373764349274,
 -0.0076327732856707516,
 -0.003359005157638993,
 0.0064289012241005097, 
-0.013430000000003162, 
-0.0029959999999995546,
 -0.0065307135571379222,
 -0.006605572447413598,
 -0.0099422652522889073,
 -0.015080331241097611,
 -0.0016757131155144375,
 -0.010765855482435674,
 -0.0028346121922537357,
 -0.014091061276246888,
 -0.0014857985251928623,
 -0.0056375351611077946,
 -0.011988911430201157,
 -0.0049400354875454924,
 -0.0099028010321836699,
 -0.0045315332341146703,
 -0.018321444937884485,
 -0.0050991387310010752,
 -0.027683215530298805,
 0.0015174037330767526,
 -0.0075530851759402738,
 0.019037454812601148,
 0.00020298122212324523, 
0.0081699113196296563,
 -0.0011547055231802498,
 0.0043124328279300489,
 -0.0014283591672329676,
 0.0029302575544578394,
 -0.001462892683058185,
 0.0018357150212062624,
 -0.0014666841715850814,
 0.00088237880086386444, 
-0.0014699999999976399,
 0.0]

我已經嘗試了多種方法，但是我沒有任何想法知道我可能做錯了什么？ 我從沒在ios上使用過FFT功能，也沒有檢查過文檔，在這種情況下似乎沒有幫助。

Answer 1

發現得好。

比例因子2 是Apple實際FFT實現的一個屬性 。 不知道為什么會這樣，也許效率更高。