libfft.h

实现ipvlbi数据记录

/*  cdft偼俀侽侽侾丏俋丏侾俉尰嵼FFT偺惓偟偄摎偊傪弌偡偙偲傪
妋擣偟偰偄傑偡  T.KONDO
*/

#ifndef _LIBFFT_
#define _LIBFFT_


#ifndef PIRA
#define PIRA  1.745329252E-2    // PI/180  degree to radian
#endif

void hanning(double *cdata,int nfft);  // hanning prototype


/*
Fast Fourier/Cosine/Sine Transform
    dimension   :one
    data length :power of 2
    decimation  :frequency
    radix       :4, 2
    data        :inplace
    table       :not use
functions
    cdft: Complex Discrete Fourier Transform
    rdft: Real Discrete Fourier Transform
    ddct: Discrete Cosine Transform
    ddst: Discrete Sine Transform
    dfct: Cosine Transform of RDFT (Real Symmetric DFT)
    dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
function prototypes
    void cdft(int, int, double *);
    void rdft(int, int, double *);
    void ddct(int, int, double *);
    void ddst(int, int, double *);
    void dfct(int, double *);
    void dfst(int, double *);


-------- Complex DFT (Discrete Fourier Transform) --------
    [definition]
        <case1>
            X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
        <case2>
            X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
        (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
    [usage]
        <case1>
            cdft(2*n, 1, a);
        <case2>
            cdft(2*n, -1, a);
    [parameters]
        2*n            :data length (int)
                        n >= 1, n = power of 2
        a[0...2*n-1]   :input/output data (double *)
                        input data
                            a[2*j] = Re(x[j]), 
                            a[2*j+1] = Im(x[j]), 0<=j<n
                        output data
                            a[2*k] = Re(X[k]), 
                            a[2*k+1] = Im(X[k]), 0<=k<n
    [remark]
        Inverse of 
            cdft(2*n, -1, a);
        is 
            cdft(2*n, 1, a);
            for (j = 0; j <= 2 * n - 1; j++) {
                a[j] *= 1.0 / n;
            }
        .


-------- Real DFT / Inverse of Real DFT --------
    [definition]
        <case1> RDFT
            R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
            I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
        <case2> IRDFT (excluding scale)
            a[k] = (R[0] + R[n/2]*cos(pi*k))/2 + 
                   sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) + 
                   sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
    [usage]
        <case1>
            rdft(n, 1, a);
        <case2>
            rdft(n, -1, a);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        <case1>
                            output data
                                a[2*k] = R[k], 0<=k<n/2
                                a[2*k+1] = I[k], 0<k<n/2
                                a[1] = R[n/2]
                        <case2>
                            input data
                                a[2*j] = R[j], 0<=j<n/2
                                a[2*j+1] = I[j], 0<j<n/2
                                a[1] = R[n/2]
    [remark]
        Inverse of 
            rdft(n, 1, a);
        is 
            rdft(n, -1, a);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
    [definition]
        <case1> IDCT (excluding scale)
            C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DCT
            C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
    [usage]
        <case1>
            ddct(n, 1, a);
        <case2>
            ddct(n, -1, a);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        output data
                            a[k] = C[k], 0<=k<n
    [remark]
        Inverse of 
            ddct(n, -1, a);
        is 
            a[0] *= 0.5;
            ddct(n, 1, a);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DST (Discrete Sine Transform) / Inverse of DST --------
    [definition]
        <case1> IDST (excluding scale)
            S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DST
            S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
    [usage]
        <case1>
            ddst(n, 1, a);
        <case2>
            ddst(n, -1, a);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        <case1>
                            input data
                                a[j] = A[j], 0<j<n
                                a[0] = A[n]
                            output data
                                a[k] = S[k], 0<=k<n
                        <case2>
                            output data
                                a[k] = S[k], 0<k<n
                                a[0] = S[n]
    [remark]
        Inverse of 
            ddst(n, -1, a);
        is 
            a[0] *= 0.5;
            ddst(n, 1, a);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
    [definition]
        C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
    [usage]
        dfct(n, a);
    [parameters]
        n              :data length - 1 (int)
                        n >= 2, n = power of 2
        a[0...n]       :input/output data (double *)
                        output data
                            a[k] = C[k], 0<=k<=n
    [remark]
        Inverse of 
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a);
        is 
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a);
            for (j = 0; j <= n; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
    [definition]
        S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
    [usage]
        dfst(n, a);
    [parameters]
        n              :data length + 1 (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        output data
                            a[k] = S[k], 0<k<n
                        (a[0] is used for work area)
    [remark]
        Inverse of 
            dfst(n, a);
        is 
            dfst(n, a);
            for (j = 1; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .
*/


void cdft(int n, int isgn, double *a)
{
    void bitrv2(int n, double *a);
    void bitrv2conj(int n, double *a);
    void cftfsub(int n, double *a);
    void cftbsub(int n, double *a);
    int j;
    if (n > 4) {
        if (isgn >= 0) {
            bitrv2(n, a);
            cftfsub(n, a);
        } else {
            bitrv2conj(n, a);
            cftbsub(n, a);
        }
    } else if (n == 4) {
        cftfsub(n, a);
    }
	/* 埲壓偼媡曄姺偺帪偵PV-WAVE 偲掕媊傪崌傢偣傞偨傔捛壛(kondo) */
	if (isgn < 0){
		for (j = 0; j <= 2 * (n/2) - 1; j++) {
           a[j] *= 1.0 / (n/2);
		}	
	}
}


void rdft(int n, int isgn, double *a)
{
    void bitrv2(int n, double *a);
    void cftfsub(int n, double *a);
    void cftbsub(int n, double *a);
    void rftfsub(int n, double *a);
    void rftbsub(int n, double *a);
    double xi;
    
    if (isgn >= 0) {
        if (n > 4) {
            bitrv2(n, a);
            cftfsub(n, a);
            rftfsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
        xi = a[0] - a[1];
        a[0] += a[1];
        a[1] = xi;
    } else {
        a[1] = 0.5 * (a[0] - a[1]);
        a[0] -= a[1];
        if (n > 4) {
            rftbsub(n, a);
            bitrv2(n, a);
            cftbsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
    }
}


void ddct(int n, int isgn, double *a)
{
    void bitrv2(int n, double *a);
    void cftfsub(int n, double *a);
    void cftbsub(int n, double *a);
    void rftfsub(int n, double *a);
    void rftbsub(int n, double *a);
    void dctsub(int n, double *a);
    void dctsub4(int n, double *a);
    int j;
    double xr;
    
    if (isgn < 0) {
        xr = a[n - 1];
        for (j = n - 2; j >= 2; j -= 2) {
            a[j + 1] = a[j] - a[j - 1];
            a[j] += a[j - 1];
        }
        a[1] = a[0] - xr;
        a[0] += xr;
        if (n > 4) {
            rftbsub(n, a);
            bitrv2(n, a);
            cftbsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
    }
    if (n > 4) {
        dctsub(n, a);
    } else {
        dctsub4(n, a);
    }
    if (isgn >= 0) {
        if (n > 4) {
            bitrv2(n, a);
            cftfsub(n, a);
            rftfsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
        xr = a[0] - a[1];
        a[0] += a[1];
        for (j = 2; j < n; j += 2) {
            a[j - 1] = a[j] - a[j + 1];
            a[j] += a[j + 1];
        }
        a[n - 1] = xr;
    }
}


void ddst(int n, int isgn, double *a)
{
    void bitrv2(int n, double *a);
    void cftfsub(int n, double *a);
    void cftbsub(int n, double *a);
    void rftfsub(int n, double *a);
    void rftbsub(int n, double *a);
    void dstsub(int n, double *a);
    void dstsub4(int n, double *a);
    int j;
    double xr;
    
    if (isgn < 0) {
        xr = a[n - 1];
        for (j = n - 2; j >= 2; j -= 2) {
            a[j + 1] = -a[j] - a[j - 1];
            a[j] -= a[j - 1];
        }
        a[1] = a[0] + xr;
        a[0] -= xr;
        if (n > 4) {
            rftbsub(n, a);
            bitrv2(n, a);
            cftbsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
    }
    if (n > 4) {
        dstsub(n, a);
    } else {
        dstsub4(n, a);
    }
    if (isgn >= 0) {
        if (n > 4) {
            bitrv2(n, a);
            cftfsub(n, a);
            rftfsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
        xr = a[0] - a[1];
        a[0] += a[1];
        for (j = 2; j < n; j += 2) {
            a[j - 1] = -a[j] - a[j + 1];
            a[j] -= a[j + 1];
        }
        a[n - 1] = -xr;
    }
}


void dfct(int n, double *a)
{
    void ddct(int n, int isgn, double *a);
    void bitrv1(int n, double *a);
    int j, k, m, mh;
    double xr, xi, yr, yi, an;
    
    m = n >> 1;
    for (j = 0; j < m; j++) {
        k = n - j;
        xr = a[j] + a[k];
        a[j] -= a[k];
        a[k] = xr;
    }
    an = a[n];
    while (m >= 2) {
        ddct(m, 1, a);
        bitrv1(m, a);
        mh = m >> 1;
        xi = a[m];
        a[m] = a[0];
        a[0] = an - xi;
        an += xi;
        for (j = 1; j < mh; j++) {
            k = m - j;
            xr = a[m + k];
            xi = a[m + j];
            yr = a[j];
            yi = a[k];
            a[m + j] = yr;
            a[m + k] = yi;
            a[j] = xr - xi;
            a[k] = xr + xi;
        }
        xr = a[mh];
        a[mh] = a[m + mh];
        a[m + mh] = xr;
        m = mh;
    }
    xi = a[1];
    a[1] = a[0];
    a[0] = an + xi;
    a[n] = an - xi;
    bitrv1(n, a);
}


void dfst(int n, double *a)
{
    void ddst(int n, int isgn, double *a);
    void bitrv1(int n, double *a);
    int j, k, m, mh;
    double xr, xi, yr, yi;
    
    m = n >> 1;
    for (j = 1; j < m; j++) {
        k = n - j;
        xr = a[j] - a[k];
        a[j] += a[k];
        a[k] = xr;
    }
    a[0] = a[m];
    while (m >= 2) {
        ddst(m, 1, a);
        bitrv1(m, a);
        mh = m >> 1;
        for (j = 1; j < mh; j++) {
            k = m - j;
            xr = a[m + k];
            xi = a[m + j];
            yr = a[j];
            yi = a[k];
            a[m + j] = yr;
            a[m + k] = yi;
            a[j] = xr + xi;
            a[k] = xr - xi;
        }
        a[m] = a[0];