Revision 0:47be4d9de4b9, committed 2015-05-01

Comitter:

TareObjects

Date:

Fri May 01 19:26:11 2015 +0000

Child:

1:ad135c286d4d

Commit message:

connect FRDM-KL46 with AQM1248 and show spectrum of magnetic density; ; by using:; - FRDM-KL46; - innter LCD; - innter MAG3110 Three Axis, Digital Magnetometer; - AQM1248 micro Graphic LCD; - Dr. Ooura's very fast FFT library; ; thanks for all.

Changed in this revision

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MAG3110.lib	Fri May 01 19:26:11 2015 +0000
@@ -0,0 +1,1 @@
+http://mbed.org/users/SomeRandomBloke/code/MAG3110/#1da3fe7b3510

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/SLCD.lib	Fri May 01 19:26:11 2015 +0000
@@ -0,0 +1,1 @@
+http://mbed.org/users/Sissors/code/SLCD/#ef2b3b7f1b01

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/aqm1248a_lcd.lib	Fri May 01 19:26:11 2015 +0000
@@ -0,0 +1,1 @@
+http://mbed.org/users/masato/code/aqm1248a_lcd/#cecd70424890

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fft4g.cpp	Fri May 01 19:26:11 2015 +0000
@@ -0,0 +1,1346 @@
+/*
+Fast Fourier/Cosine/Sine Transform
+    dimension   :one
+    data length :power of 2
+    decimation  :frequency
+    radix       :4, 2
+    data        :inplace
+    table       :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 *, int *, double *);
+    void rdft(int, int, double *, int *, double *);
+    void ddct(int, int, double *, int *, double *);
+    void ddst(int, int, double *, int *, double *);
+    void dfct(int, double *, double *, int *, double *);
+    void dfst(int, double *, double *, 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>
+            ip[0] = 0; // first time only
+            cdft(2*n, 1, a, ip, w);
+        <case2>
+            ip[0] = 0; // first time only
+            cdft(2*n, -1, a, ip, w);
+    [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
+        ip[0...*]      :work area for bit reversal (int *)
+                        length of ip >= 2+sqrt(n)
+                        strictly, 
+                        length of ip >= 
+                            2+(1<<(int)(log(n+0.5)/log(2))/2).
+                        ip[0],ip[1] are pointers of the cos/sin table.
+        w[0...n/2-1]   :cos/sin table (double *)
+                        w[],ip[] are initialized if ip[0] == 0.
+    [remark]
+        Inverse of 
+            cdft(2*n, -1, a, ip, w);
+        is 
+            cdft(2*n, 1, a, ip, w);
+            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>
+            ip[0] = 0; // first time only
+            rdft(n, 1, a, ip, w);
+        <case2>
+            ip[0] = 0; // first time only
+            rdft(n, -1, a, ip, w);
+    [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]
+        ip[0...*]      :work area for bit reversal (int *)
+                        length of ip >= 2+sqrt(n/2)
+                        strictly, 
+                        length of ip >= 
+                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+                        ip[0],ip[1] are pointers of the cos/sin table.
+        w[0...n/2-1]   :cos/sin table (double *)
+                        w[],ip[] are initialized if ip[0] == 0.
+    [remark]
+        Inverse of 
+            rdft(n, 1, a, ip, w);
+        is 
+            rdft(n, -1, a, ip, w);
+            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>
+            ip[0] = 0; // first time only
+            ddct(n, 1, a, ip, w);
+        <case2>
+            ip[0] = 0; // first time only
+            ddct(n, -1, a, ip, w);
+    [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
+        ip[0...*]      :work area for bit reversal (int *)
+                        length of ip >= 2+sqrt(n/2)
+                        strictly, 
+                        length of ip >= 
+                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+                        ip[0],ip[1] are pointers of the cos/sin table.
+        w[0...n*5/4-1] :cos/sin table (double *)
+                        w[],ip[] are initialized if ip[0] == 0.
+    [remark]
+        Inverse of 
+            ddct(n, -1, a, ip, w);
+        is 
+            a[0] *= 0.5;
+            ddct(n, 1, a, ip, w);
+            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>
+            ip[0] = 0; // first time only
+            ddst(n, 1, a, ip, w);
+        <case2>
+            ip[0] = 0; // first time only
+            ddst(n, -1, a, ip, w);
+    [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]
+        ip[0...*]      :work area for bit reversal (int *)
+                        length of ip >= 2+sqrt(n/2)
+                        strictly, 
+                        length of ip >= 
+                            2+(1<<(int)(log(n/2+0.5)/log(2))/2).
+                        ip[0],ip[1] are pointers of the cos/sin table.
+        w[0...n*5/4-1] :cos/sin table (double *)
+                        w[],ip[] are initialized if ip[0] == 0.
+    [remark]
+        Inverse of 
+            ddst(n, -1, a, ip, w);
+        is 
+            a[0] *= 0.5;
+            ddst(n, 1, a, ip, w);
+            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]
+        ip[0] = 0; // first time only
+        dfct(n, a, t, ip, w);
+    [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
+        t[0...n/2]     :work area (double *)
+        ip[0...*]      :work area for bit reversal (int *)
+                        length of ip >= 2+sqrt(n/4)
+                        strictly, 
+                        length of ip >= 
+                            2+(1<<(int)(log(n/4+0.5)/log(2))/2).
+                        ip[0],ip[1] are pointers of the cos/sin table.
+        w[0...n*5/8-1] :cos/sin table (double *)
+                        w[],ip[] are initialized if ip[0] == 0.
+    [remark]
+        Inverse of 
+            a[0] *= 0.5;
+            a[n] *= 0.5;
+            dfct(n, a, t, ip, w);
+        is 
+            a[0] *= 0.5;
+            a[n] *= 0.5;
+            dfct(n, a, t, ip, w);
+            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]
+        ip[0] = 0; // first time only
+        dfst(n, a, t, ip, w);
+    [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)
+        t[0...n/2-1]   :work area (double *)
+        ip[0...*]      :work area for bit reversal (int *)
+                        length of ip >= 2+sqrt(n/4)
+                        strictly, 
+                        length of ip >= 
+                            2+(1<<(int)(log(n/4+0.5)/log(2))/2).
+                        ip[0],ip[1] are pointers of the cos/sin table.
+        w[0...n*5/8-1] :cos/sin table (double *)
+                        w[],ip[] are initialized if ip[0] == 0.
+    [remark]
+        Inverse of 
+            dfst(n, a, t, ip, w);
+        is 
+            dfst(n, a, t, ip, w);
+            for (j = 1; j <= n - 1; j++) {
+                a[j] *= 2.0 / n;
+            }
+        .
+
+
+Appendix :
+    The cos/sin table is recalculated when the larger table required.
+    w[] and ip[] are compatible with all routines.
+*/
+
+
+void cdft(int n, int isgn, double *a, int *ip, double *w)
+{
+    void makewt(int nw, int *ip, double *w);
+    void bitrv2(int n, int *ip, double *a);
+    void bitrv2conj(int n, int *ip, double *a);
+    void cftfsub(int n, double *a, double *w);
+    void cftbsub(int n, double *a, double *w);
+    
+    if (n > (ip[0] << 2)) {
+        makewt(n >> 2, ip, w);
+    }
+    if (n > 4) {
+        if (isgn >= 0) {
+            bitrv2(n, ip + 2, a);
+            cftfsub(n, a, w);
+        } else {
+            bitrv2conj(n, ip + 2, a);
+            cftbsub(n, a, w);
+        }
+    } else if (n == 4) {
+        cftfsub(n, a, w);
+    }
+}
+
+
+void rdft(int n, int isgn, double *a, int *ip, double *w)
+{
+    void makewt(int nw, int *ip, double *w);
+    void makect(int nc, int *ip, double *c);
+    void bitrv2(int n, int *ip, double *a);
+    void cftfsub(int n, double *a, double *w);
+    void cftbsub(int n, double *a, double *w);
+    void rftfsub(int n, double *a, int nc, double *c);
+    void rftbsub(int n, double *a, int nc, double *c);
+    int nw, nc;
+    double xi;
+    
+    nw = ip[0];
+    if (n > (nw << 2)) {
+        nw = n >> 2;
+        makewt(nw, ip, w);
+    }
+    nc = ip[1];
+    if (n > (nc << 2)) {
+        nc = n >> 2;
+        makect(nc, ip, w + nw);
+    }
+    if (isgn >= 0) {
+        if (n > 4) {
+            bitrv2(n, ip + 2, a);
+            cftfsub(n, a, w);
+            rftfsub(n, a, nc, w + nw);
+        } else if (n == 4) {
+            cftfsub(n, a, w);
+        }
+        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, nc, w + nw);
+            bitrv2(n, ip + 2, a);
+            cftbsub(n, a, w);
+        } else if (n == 4) {
+            cftfsub(n, a, w);
+        }
+    }
+}
+
+
+void ddct(int n, int isgn, double *a, int *ip, double *w)
+{
+    void makewt(int nw, int *ip, double *w);
+    void makect(int nc, int *ip, double *c);
+    void bitrv2(int n, int *ip, double *a);
+    void cftfsub(int n, double *a, double *w);
+    void cftbsub(int n, double *a, double *w);
+    void rftfsub(int n, double *a, int nc, double *c);
+    void rftbsub(int n, double *a, int nc, double *c);
+    void dctsub(int n, double *a, int nc, double *c);
+    int j, nw, nc;
+    double xr;
+    
+    nw = ip[0];
+    if (n > (nw << 2)) {
+        nw = n >> 2;
+        makewt(nw, ip, w);
+    }
+    nc = ip[1];
+    if (n > nc) {
+        nc = n;
+        makect(nc, ip, w + nw);
+    }
+    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, nc, w + nw);
+            bitrv2(n, ip + 2, a);
+            cftbsub(n, a, w);
+        } else if (n == 4) {
+            cftfsub(n, a, w);
+        }
+    }
+    dctsub(n, a, nc, w + nw);
+    if (isgn >= 0) {
+        if (n > 4) {
+            bitrv2(n, ip + 2, a);
+            cftfsub(n, a, w);
+            rftfsub(n, a, nc, w + nw);
+        } else if (n == 4) {
+            cftfsub(n, a, w);
+        }
+        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, int *ip, double *w)
+{
+    void makewt(int nw, int *ip, double *w);
+    void makect(int nc, int *ip, double *c);
+    void bitrv2(int n, int *ip, double *a);
+    void cftfsub(int n, double *a, double *w);
+    void cftbsub(int n, double *a, double *w);
+    void rftfsub(int n, double *a, int nc, double *c);
+    void rftbsub(int n, double *a, int nc, double *c);
+    void dstsub(int n, double *a, int nc, double *c);
+    int j, nw, nc;
+    double xr;
+    
+    nw = ip[0];
+    if (n > (nw << 2)) {
+        nw = n >> 2;
+        makewt(nw, ip, w);
+    }
+    nc = ip[1];
+    if (n > nc) {
+        nc = n;
+        makect(nc, ip, w + nw);
+    }
+    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, nc, w + nw);
+            bitrv2(n, ip + 2, a);
+            cftbsub(n, a, w);
+        } else if (n == 4) {
+            cftfsub(n, a, w);
+        }
+    }
+    dstsub(n, a, nc, w + nw);
+    if (isgn >= 0) {
+        if (n > 4) {
+            bitrv2(n, ip + 2, a);
+            cftfsub(n, a, w);
+            rftfsub(n, a, nc, w + nw);
+        } else if (n == 4) {
+            cftfsub(n, a, w);
+        }
+        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, double *t, int *ip, double *w)
+{
+    void makewt(int nw, int *ip, double *w);
+    void makect(int nc, int *ip, double *c);
+    void bitrv2(int n, int *ip, double *a);
+    void cftfsub(int n, double *a, double *w);
+    void rftfsub(int n, double *a, int nc, double *c);
+    void dctsub(int n, double *a, int nc, double *c);
+    int j, k, l, m, mh, nw, nc;
+    double xr, xi, yr, yi;
+    
+    nw = ip[0];
+    if (n > (nw << 3)) {
+        nw = n >> 3;
+        makewt(nw, ip, w);
+    }
+    nc = ip[1];
+    if (n > (nc << 1)) {
+        nc = n >> 1;
+        makect(nc, ip, w + nw);
+    }
+    m = n >> 1;
+    yi = a[m];
+    xi = a[0] + a[n];
+    a[0] -= a[n];
+    t[0] = xi - yi;
+    t[m] = xi + yi;
+    if (n > 2) {
+        mh = m >> 1;
+        for (j = 1; j < mh; j++) {
+            k = m - j;
+            xr = a[j] - a[n - j];
+            xi = a[j] + a[n - j];
+            yr = a[k] - a[n - k];
+            yi = a[k] + a[n - k];
+            a[j] = xr;
+            a[k] = yr;
+            t[j] = xi - yi;
+            t[k] = xi + yi;
+        }
+        t[mh] = a[mh] + a[n - mh];
+        a[mh] -= a[n - mh];
+        dctsub(m, a, nc, w + nw);
+        if (m > 4) {
+            bitrv2(m, ip + 2, a);
+            cftfsub(m, a, w);
+            rftfsub(m, a, nc, w + nw);
+        } else if (m == 4) {
+            cftfsub(m, a, w);
+        }
+        a[n - 1] = a[0] - a[1];
+        a[1] = a[0] + a[1];
+        for (j = m - 2; j >= 2; j -= 2) {
+            a[2 * j + 1] = a[j] + a[j + 1];
+            a[2 * j - 1] = a[j] - a[j + 1];
+        }
+        l = 2;
+        m = mh;
+        while (m >= 2) {
+            dctsub(m, t, nc, w + nw);
+            if (m > 4) {
+                bitrv2(m, ip + 2, t);
+                cftfsub(m, t, w);
+                rftfsub(m, t, nc, w + nw);
+            } else if (m == 4) {
+                cftfsub(m, t, w);
+            }
+            a[n - l] = t[0] - t[1];
+            a[l] = t[0] + t[1];
+            k = 0;
+            for (j = 2; j < m; j += 2) {
+                k += l << 2;
+                a[k - l] = t[j] - t[j + 1];
+                a[k + l] = t[j] + t[j + 1];
+            }
+            l <<= 1;
+            mh = m >> 1;
+            for (j = 0; j < mh; j++) {
+                k = m - j;
+                t[j] = t[m + k] - t[m + j];
+                t[k] = t[m + k] + t[m + j];
+            }
+            t[mh] = t[m + mh];
+            m = mh;
+        }
+        a[l] = t[0];
+        a[n] = t[2] - t[1];
+        a[0] = t[2] + t[1];
+    } else {
+        a[1] = a[0];
+        a[2] = t[0];
+        a[0] = t[1];
+    }
+}
+
+
+void dfst(int n, double *a, double *t, int *ip, double *w)
+{
+    void makewt(int nw, int *ip, double *w);
+    void makect(int nc, int *ip, double *c);
+    void bitrv2(int n, int *ip, double *a);
+    void cftfsub(int n, double *a, double *w);
+    void rftfsub(int n, double *a, int nc, double *c);
+    void dstsub(int n, double *a, int nc, double *c);
+    int j, k, l, m, mh, nw, nc;
+    double xr, xi, yr, yi;
+    
+    nw = ip[0];
+    if (n > (nw << 3)) {
+        nw = n >> 3;
+        makewt(nw, ip, w);
+    }
+    nc = ip[1];
+    if (n > (nc << 1)) {
+        nc = n >> 1;
+        makect(nc, ip, w + nw);
+    }
+    if (n > 2) {
+        m = n >> 1;
+        mh = m >> 1;
+        for (j = 1; j < mh; j++) {
+            k = m - j;
+            xr = a[j] + a[n - j];
+            xi = a[j] - a[n - j];
+            yr = a[k] + a[n - k];
+            yi = a[k] - a[n - k];
+            a[j] = xr;
+            a[k] = yr;
+            t[j] = xi + yi;
+            t[k] = xi - yi;
+        }
+        t[0] = a[mh] - a[n - mh];
+        a[mh] += a[n - mh];
+        a[0] = a[m];
+        dstsub(m, a, nc, w + nw);
+        if (m > 4) {
+            bitrv2(m, ip + 2, a);
+            cftfsub(m, a, w);
+            rftfsub(m, a, nc, w + nw);
+        } else if (m == 4) {
+            cftfsub(m, a, w);
+        }
+        a[n - 1] = a[1] - a[0];
+        a[1] = a[0] + a[1];
+        for (j = m - 2; j >= 2; j -= 2) {
+            a[2 * j + 1] = a[j] - a[j + 1];
+            a[2 * j - 1] = -a[j] - a[j + 1];
+        }
+        l = 2;
+        m = mh;
+        while (m >= 2) {
+            dstsub(m, t, nc, w + nw);
+            if (m > 4) {
+                bitrv2(m, ip + 2, t);
+                cftfsub(m, t, w);
+                rftfsub(m, t, nc, w + nw);
+            } else if (m == 4) {
+                cftfsub(m, t, w);
+            }
+            a[n - l] = t[1] - t[0];
+            a[l] = t[0] + t[1];
+            k = 0;
+            for (j = 2; j < m; j += 2) {
+                k += l << 2;
+                a[k - l] = -t[j] - t[j + 1];
+                a[k + l] = t[j] - t[j + 1];
+            }
+            l <<= 1;
+            mh = m >> 1;
+            for (j = 1; j < mh; j++) {
+                k = m - j;
+                t[j] = t[m + k] + t[m + j];
+                t[k] = t[m + k] - t[m + j];
+            }
+            t[0] = t[m + mh];
+            m = mh;
+        }
+        a[l] = t[0];
+    }
+    a[0] = 0;
+}
+
+
+/* -------- initializing routines -------- */
+
+
+#include <math.h>
+
+void makewt(int nw, int *ip, double *w)
+{
+    void bitrv2(int n, int *ip, double *a);
+    int j, nwh;
+    double delta, x, y;
+    
+    ip[0] = nw;
+    ip[1] = 1;
+    if (nw > 2) {
+        nwh = nw >> 1;
+        delta = atan(1.0) / nwh;
+        w[0] = 1;
+        w[1] = 0;
+        w[nwh] = cos(delta * nwh);
+        w[nwh + 1] = w[nwh];
+        if (nwh > 2) {
+            for (j = 2; j < nwh; j += 2) {
+                x = cos(delta * j);
+                y = sin(delta * j);
+                w[j] = x;
+                w[j + 1] = y;
+                w[nw - j] = y;
+                w[nw - j + 1] = x;
+            }
+            bitrv2(nw, ip + 2, w);
+        }
+    }
+}
+
+
+void makect(int nc, int *ip, double *c)
+{
+    int j, nch;
+    double delta;
+    
+    ip[1] = nc;
+    if (nc > 1) {
+        nch = nc >> 1;
+        delta = atan(1.0) / nch;
+        c[0] = cos(delta * nch);
+        c[nch] = 0.5 * c[0];
+        for (j = 1; j < nch; j++) {
+            c[j] = 0.5 * cos(delta * j);
+            c[nc - j] = 0.5 * sin(delta * j);
+        }
+    }
+}
+
+
+/* -------- child routines -------- */
+
+
+void bitrv2(int n, int *ip, double *a)
+{
+    int j, j1, k, k1, l, m, m2;
+    double xr, xi, yr, yi;
+    
+    ip[0] = 0;
+    l = n;
+    m = 1;
+    while ((m << 3) < l) {
+        l >>= 1;
+        for (j = 0; j < m; j++) {
+            ip[m + j] = ip[j] + l;
+        }
+        m <<= 1;
+    }
+    m2 = 2 * m;
+    if ((m << 3) == l) {
+        for (k = 0; k < m; k++) {
+            for (j = 0; j < k; j++) {
+                j1 = 2 * j + ip[k];
+                k1 = 2 * k + ip[j];
+                xr = a[j1];
+                xi = a[j1 + 1];
+                yr = a[k1];
+                yi = a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+                j1 += m2;
+                k1 += 2 * m2;
+                xr = a[j1];
+                xi = a[j1 + 1];
+                yr = a[k1];
+                yi = a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+                j1 += m2;
+                k1 -= m2;
+                xr = a[j1];
+                xi = a[j1 + 1];
+                yr = a[k1];
+                yi = a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+                j1 += m2;
+                k1 += 2 * m2;
+                xr = a[j1];
+                xi = a[j1 + 1];
+                yr = a[k1];
+                yi = a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+            }
+            j1 = 2 * k + m2 + ip[k];
+            k1 = j1 + m2;
+            xr = a[j1];
+            xi = a[j1 + 1];
+            yr = a[k1];
+            yi = a[k1 + 1];
+            a[j1] = yr;
+            a[j1 + 1] = yi;
+            a[k1] = xr;
+            a[k1 + 1] = xi;
+        }
+    } else {
+        for (k = 1; k < m; k++) {
+            for (j = 0; j < k; j++) {
+                j1 = 2 * j + ip[k];
+                k1 = 2 * k + ip[j];
+                xr = a[j1];
+                xi = a[j1 + 1];
+                yr = a[k1];
+                yi = a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+                j1 += m2;
+                k1 += m2;
+                xr = a[j1];
+                xi = a[j1 + 1];
+                yr = a[k1];
+                yi = a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+            }
+        }
+    }
+}
+
+
+void bitrv2conj(int n, int *ip, double *a)
+{
+    int j, j1, k, k1, l, m, m2;
+    double xr, xi, yr, yi;
+    
+    ip[0] = 0;
+    l = n;
+    m = 1;
+    while ((m << 3) < l) {
+        l >>= 1;
+        for (j = 0; j < m; j++) {
+            ip[m + j] = ip[j] + l;
+        }
+        m <<= 1;
+    }
+    m2 = 2 * m;
+    if ((m << 3) == l) {
+        for (k = 0; k < m; k++) {
+            for (j = 0; j < k; j++) {
+                j1 = 2 * j + ip[k];
+                k1 = 2 * k + ip[j];
+                xr = a[j1];
+                xi = -a[j1 + 1];
+                yr = a[k1];
+                yi = -a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+                j1 += m2;
+                k1 += 2 * m2;
+                xr = a[j1];
+                xi = -a[j1 + 1];
+                yr = a[k1];
+                yi = -a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+                j1 += m2;
+                k1 -= m2;
+                xr = a[j1];
+                xi = -a[j1 + 1];
+                yr = a[k1];
+                yi = -a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+                j1 += m2;
+                k1 += 2 * m2;
+                xr = a[j1];
+                xi = -a[j1 + 1];
+                yr = a[k1];
+                yi = -a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+            }
+            k1 = 2 * k + ip[k];
+            a[k1 + 1] = -a[k1 + 1];
+            j1 = k1 + m2;
+            k1 = j1 + m2;
+            xr = a[j1];
+            xi = -a[j1 + 1];
+            yr = a[k1];
+            yi = -a[k1 + 1];
+            a[j1] = yr;
+            a[j1 + 1] = yi;
+            a[k1] = xr;
+            a[k1 + 1] = xi;
+            k1 += m2;
+            a[k1 + 1] = -a[k1 + 1];
+        }
+    } else {
+        a[1] = -a[1];
+        a[m2 + 1] = -a[m2 + 1];
+        for (k = 1; k < m; k++) {
+            for (j = 0; j < k; j++) {
+                j1 = 2 * j + ip[k];
+                k1 = 2 * k + ip[j];
+                xr = a[j1];
+                xi = -a[j1 + 1];
+                yr = a[k1];
+                yi = -a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+                j1 += m2;
+                k1 += m2;
+                xr = a[j1];
+                xi = -a[j1 + 1];
+                yr = a[k1];
+                yi = -a[k1 + 1];
+                a[j1] = yr;
+                a[j1 + 1] = yi;
+                a[k1] = xr;
+                a[k1 + 1] = xi;
+            }
+            k1 = 2 * k + ip[k];
+            a[k1 + 1] = -a[k1 + 1];
+            a[k1 + m2 + 1] = -a[k1 + m2 + 1];
+        }
+    }
+}
+
+
+void cftfsub(int n, double *a, double *w)
+{
+    void cft1st(int n, double *a, double *w);
+    void cftmdl(int n, int l, double *a, double *w);
+    int j, j1, j2, j3, l;
+    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+    
+    l = 2;
+    if (n > 8) {
+        cft1st(n, a, w);
+        l = 8;
+        while ((l << 2) < n) {
+            cftmdl(n, l, a, w);
+            l <<= 2;
+        }
+    }
+    if ((l << 2) == n) {
+        for (j = 0; j < l; j += 2) {
+            j1 = j + l;
+            j2 = j1 + l;
+            j3 = j2 + l;
+            x0r = a[j] + a[j1];
+            x0i = a[j + 1] + a[j1 + 1];
+            x1r = a[j] - a[j1];
+            x1i = a[j + 1] - a[j1 + 1];
+            x2r = a[j2] + a[j3];
+            x2i = a[j2 + 1] + a[j3 + 1];
+            x3r = a[j2] - a[j3];
+            x3i = a[j2 + 1] - a[j3 + 1];
+            a[j] = x0r + x2r;
+            a[j + 1] = x0i + x2i;
+            a[j2] = x0r - x2r;
+            a[j2 + 1] = x0i - x2i;
+            a[j1] = x1r - x3i;
+            a[j1 + 1] = x1i + x3r;
+            a[j3] = x1r + x3i;
+            a[j3 + 1] = x1i - x3r;
+        }
+    } else {
+        for (j = 0; j < l; j += 2) {
+            j1 = j + l;
+            x0r = a[j] - a[j1];
+            x0i = a[j + 1] - a[j1 + 1];
+            a[j] += a[j1];
+            a[j + 1] += a[j1 + 1];
+            a[j1] = x0r;
+            a[j1 + 1] = x0i;
+        }
+    }
+}
+
+
+void cftbsub(int n, double *a, double *w)
+{
+    void cft1st(int n, double *a, double *w);
+    void cftmdl(int n, int l, double *a, double *w);
+    int j, j1, j2, j3, l;
+    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+    
+    l = 2;
+    if (n > 8) {
+        cft1st(n, a, w);
+        l = 8;
+        while ((l << 2) < n) {
+            cftmdl(n, l, a, w);
+            l <<= 2;
+        }
+    }
+    if ((l << 2) == n) {
+        for (j = 0; j < l; j += 2) {
+            j1 = j + l;
+            j2 = j1 + l;
+            j3 = j2 + l;
+            x0r = a[j] + a[j1];
+            x0i = -a[j + 1] - a[j1 + 1];
+            x1r = a[j] - a[j1];
+            x1i = -a[j + 1] + a[j1 + 1];
+            x2r = a[j2] + a[j3];
+            x2i = a[j2 + 1] + a[j3 + 1];
+            x3r = a[j2] - a[j3];
+            x3i = a[j2 + 1] - a[j3 + 1];
+            a[j] = x0r + x2r;
+            a[j + 1] = x0i - x2i;
+            a[j2] = x0r - x2r;
+            a[j2 + 1] = x0i + x2i;
+            a[j1] = x1r - x3i;
+            a[j1 + 1] = x1i - x3r;
+            a[j3] = x1r + x3i;
+            a[j3 + 1] = x1i + x3r;
+        }
+    } else {
+        for (j = 0; j < l; j += 2) {
+            j1 = j + l;
+            x0r = a[j] - a[j1];
+            x0i = -a[j + 1] + a[j1 + 1];
+            a[j] += a[j1];
+            a[j + 1] = -a[j + 1] - a[j1 + 1];
+            a[j1] = x0r;
+            a[j1 + 1] = x0i;
+        }
+    }
+}
+
+
+void cft1st(int n, double *a, double *w)
+{
+    int j, k1, k2;
+    double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
+    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+    
+    x0r = a[0] + a[2];
+    x0i = a[1] + a[3];
+    x1r = a[0] - a[2];
+    x1i = a[1] - a[3];
+    x2r = a[4] + a[6];
+    x2i = a[5] + a[7];
+    x3r = a[4] - a[6];
+    x3i = a[5] - a[7];
+    a[0] = x0r + x2r;
+    a[1] = x0i + x2i;
+    a[4] = x0r - x2r;
+    a[5] = x0i - x2i;
+    a[2] = x1r - x3i;
+    a[3] = x1i + x3r;
+    a[6] = x1r + x3i;
+    a[7] = x1i - x3r;
+    wk1r = w[2];
+    x0r = a[8] + a[10];
+    x0i = a[9] + a[11];
+    x1r = a[8] - a[10];
+    x1i = a[9] - a[11];
+    x2r = a[12] + a[14];
+    x2i = a[13] + a[15];
+    x3r = a[12] - a[14];
+    x3i = a[13] - a[15];
+    a[8] = x0r + x2r;
+    a[9] = x0i + x2i;
+    a[12] = x2i - x0i;
+    a[13] = x0r - x2r;
+    x0r = x1r - x3i;
+    x0i = x1i + x3r;
+    a[10] = wk1r * (x0r - x0i);
+    a[11] = wk1r * (x0r + x0i);
+    x0r = x3i + x1r;
+    x0i = x3r - x1i;
+    a[14] = wk1r * (x0i - x0r);
+    a[15] = wk1r * (x0i + x0r);
+    k1 = 0;
+    for (j = 16; j < n; j += 16) {
+        k1 += 2;
+        k2 = 2 * k1;
+        wk2r = w[k1];
+        wk2i = w[k1 + 1];
+        wk1r = w[k2];
+        wk1i = w[k2 + 1];
+        wk3r = wk1r - 2 * wk2i * wk1i;
+        wk3i = 2 * wk2i * wk1r - wk1i;
+        x0r = a[j] + a[j + 2];
+        x0i = a[j + 1] + a[j + 3];
+        x1r = a[j] - a[j + 2];
+        x1i = a[j + 1] - a[j + 3];
+        x2r = a[j + 4] + a[j + 6];
+        x2i = a[j + 5] + a[j + 7];
+        x3r = a[j + 4] - a[j + 6];
+        x3i = a[j + 5] - a[j + 7];
+        a[j] = x0r + x2r;
+        a[j + 1] = x0i + x2i;
+        x0r -= x2r;
+        x0i -= x2i;
+        a[j + 4] = wk2r * x0r - wk2i * x0i;
+        a[j + 5] = wk2r * x0i + wk2i * x0r;
+        x0r = x1r - x3i;
+        x0i = x1i + x3r;
+        a[j + 2] = wk1r * x0r - wk1i * x0i;
+        a[j + 3] = wk1r * x0i + wk1i * x0r;
+        x0r = x1r + x3i;
+        x0i = x1i - x3r;
+        a[j + 6] = wk3r * x0r - wk3i * x0i;
+        a[j + 7] = wk3r * x0i + wk3i * x0r;
+        wk1r = w[k2 + 2];
+        wk1i = w[k2 + 3];
+        wk3r = wk1r - 2 * wk2r * wk1i;
+        wk3i = 2 * wk2r * wk1r - wk1i;
+        x0r = a[j + 8] + a[j + 10];
+        x0i = a[j + 9] + a[j + 11];
+        x1r = a[j + 8] - a[j + 10];
+        x1i = a[j + 9] - a[j + 11];
+        x2r = a[j + 12] + a[j + 14];
+        x2i = a[j + 13] + a[j + 15];
+        x3r = a[j + 12] - a[j + 14];
+        x3i = a[j + 13] - a[j + 15];
+        a[j + 8] = x0r + x2r;
+        a[j + 9] = x0i + x2i;
+        x0r -= x2r;
+        x0i -= x2i;
+        a[j + 12] = -wk2i * x0r - wk2r * x0i;
+        a[j + 13] = -wk2i * x0i + wk2r * x0r;
+        x0r = x1r - x3i;
+        x0i = x1i + x3r;
+        a[j + 10] = wk1r * x0r - wk1i * x0i;
+        a[j + 11] = wk1r * x0i + wk1i * x0r;
+        x0r = x1r + x3i;
+        x0i = x1i - x3r;
+        a[j + 14] = wk3r * x0r - wk3i * x0i;
+        a[j + 15] = wk3r * x0i + wk3i * x0r;
+    }
+}
+
+
+void cftmdl(int n, int l, double *a, double *w)
+{
+    int j, j1, j2, j3, k, k1, k2, m, m2;
+    double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
+    double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+    
+    m = l << 2;
+    for (j = 0; j < l; j += 2) {
+        j1 = j + l;
+        j2 = j1 + l;
+        j3 = j2 + l;
+        x0r = a[j] + a[j1];
+        x0i = a[j + 1] + a[j1 + 1];
+        x1r = a[j] - a[j1];
+        x1i = a[j + 1] - a[j1 + 1];
+        x2r = a[j2] + a[j3];
+        x2i = a[j2 + 1] + a[j3 + 1];
+        x3r = a[j2] - a[j3];
+        x3i = a[j2 + 1] - a[j3 + 1];
+        a[j] = x0r + x2r;
+        a[j + 1] = x0i + x2i;
+        a[j2] = x0r - x2r;
+        a[j2 + 1] = x0i - x2i;
+        a[j1] = x1r - x3i;
+        a[j1 + 1] = x1i + x3r;
+        a[j3] = x1r + x3i;
+        a[j3 + 1] = x1i - x3r;
+    }
+    wk1r = w[2];
+    for (j = m; j < l + m; j += 2) {
+        j1 = j + l;
+        j2 = j1 + l;
+        j3 = j2 + l;
+        x0r = a[j] + a[j1];
+        x0i = a[j + 1] + a[j1 + 1];
+        x1r = a[j] - a[j1];
+        x1i = a[j + 1] - a[j1 + 1];
+        x2r = a[j2] + a[j3];
+        x2i = a[j2 + 1] + a[j3 + 1];
+        x3r = a[j2] - a[j3];
+        x3i = a[j2 + 1] - a[j3 + 1];
+        a[j] = x0r + x2r;
+        a[j + 1] = x0i + x2i;
+        a[j2] = x2i - x0i;
+        a[j2 + 1] = x0r - x2r;
+        x0r = x1r - x3i;
+        x0i = x1i + x3r;
+        a[j1] = wk1r * (x0r - x0i);
+        a[j1 + 1] = wk1r * (x0r + x0i);
+        x0r = x3i + x1r;
+        x0i = x3r - x1i;
+        a[j3] = wk1r * (x0i - x0r);
+        a[j3 + 1] = wk1r * (x0i + x0r);
+    }
+    k1 = 0;
+    m2 = 2 * m;
+    for (k = m2; k < n; k += m2) {
+        k1 += 2;
+        k2 = 2 * k1;
+        wk2r = w[k1];
+        wk2i = w[k1 + 1];
+        wk1r = w[k2];
+        wk1i = w[k2 + 1];
+        wk3r = wk1r - 2 * wk2i * wk1i;
+        wk3i = 2 * wk2i * wk1r - wk1i;
+        for (j = k; j < l + k; j += 2) {
+            j1 = j + l;
+            j2 = j1 + l;
+            j3 = j2 + l;
+            x0r = a[j] + a[j1];
+            x0i = a[j + 1] + a[j1 + 1];
+            x1r = a[j] - a[j1];
+            x1i = a[j + 1] - a[j1 + 1];
+            x2r = a[j2] + a[j3];
+            x2i = a[j2 + 1] + a[j3 + 1];
+            x3r = a[j2] - a[j3];
+            x3i = a[j2 + 1] - a[j3 + 1];
+            a[j] = x0r + x2r;
+            a[j + 1] = x0i + x2i;
+            x0r -= x2r;
+            x0i -= x2i;
+            a[j2] = wk2r * x0r - wk2i * x0i;
+            a[j2 + 1] = wk2r * x0i + wk2i * x0r;
+            x0r = x1r - x3i;
+            x0i = x1i + x3r;
+            a[j1] = wk1r * x0r - wk1i * x0i;
+            a[j1 + 1] = wk1r * x0i + wk1i * x0r;
+            x0r = x1r + x3i;
+            x0i = x1i - x3r;
+            a[j3] = wk3r * x0r - wk3i * x0i;
+            a[j3 + 1] = wk3r * x0i + wk3i * x0r;
+        }
+        wk1r = w[k2 + 2];
+        wk1i = w[k2 + 3];
+        wk3r = wk1r - 2 * wk2r * wk1i;
+        wk3i = 2 * wk2r * wk1r - wk1i;
+        for (j = k + m; j < l + (k + m); j += 2) {
+            j1 = j + l;
+            j2 = j1 + l;
+            j3 = j2 + l;
+            x0r = a[j] + a[j1];
+            x0i = a[j + 1] + a[j1 + 1];
+            x1r = a[j] - a[j1];
+            x1i = a[j + 1] - a[j1 + 1];
+            x2r = a[j2] + a[j3];
+            x2i = a[j2 + 1] + a[j3 + 1];
+            x3r = a[j2] - a[j3];
+            x3i = a[j2 + 1] - a[j3 + 1];
+            a[j] = x0r + x2r;
+            a[j + 1] = x0i + x2i;
+            x0r -= x2r;
+            x0i -= x2i;
+            a[j2] = -wk2i * x0r - wk2r * x0i;
+            a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
+            x0r = x1r - x3i;
+            x0i = x1i + x3r;
+            a[j1] = wk1r * x0r - wk1i * x0i;
+            a[j1 + 1] = wk1r * x0i + wk1i * x0r;
+            x0r = x1r + x3i;
+            x0i = x1i - x3r;
+            a[j3] = wk3r * x0r - wk3i * x0i;
+            a[j3 + 1] = wk3r * x0i + wk3i * x0r;
+        }
+    }
+}
+
+
+void rftfsub(int n, double *a, int nc, double *c)
+{
+    int j, k, kk, ks, m;
+    double wkr, wki, xr, xi, yr, yi;
+    
+    m = n >> 1;
+    ks = 2 * nc / m;
+    kk = 0;
+    for (j = 2; j < m; j += 2) {
+        k = n - j;
+        kk += ks;
+        wkr = 0.5 - c[nc - kk];
+        wki = c[kk];
+        xr = a[j] - a[k];
+        xi = a[j + 1] + a[k + 1];
+        yr = wkr * xr - wki * xi;
+        yi = wkr * xi + wki * xr;
+        a[j] -= yr;
+        a[j + 1] -= yi;
+        a[k] += yr;
+        a[k + 1] -= yi;
+    }
+}
+
+
+void rftbsub(int n, double *a, int nc, double *c)
+{
+    int j, k, kk, ks, m;
+    double wkr, wki, xr, xi, yr, yi;
+    
+    a[1] = -a[1];
+    m = n >> 1;
+    ks = 2 * nc / m;
+    kk = 0;
+    for (j = 2; j < m; j += 2) {
+        k = n - j;
+        kk += ks;
+        wkr = 0.5 - c[nc - kk];
+        wki = c[kk];
+        xr = a[j] - a[k];
+        xi = a[j + 1] + a[k + 1];
+        yr = wkr * xr + wki * xi;
+        yi = wkr * xi - wki * xr;
+        a[j] -= yr;
+        a[j + 1] = yi - a[j + 1];
+        a[k] += yr;
+        a[k + 1] = yi - a[k + 1];
+    }
+    a[m + 1] = -a[m + 1];
+}
+
+
+void dctsub(int n, double *a, int nc, double *c)
+{
+    int j, k, kk, ks, m;
+    double wkr, wki, xr;
+    
+    m = n >> 1;
+    ks = nc / n;
+    kk = 0;
+    for (j = 1; j < m; j++) {
+        k = n - j;
+        kk += ks;
+        wkr = c[kk] - c[nc - kk];
+        wki = c[kk] + c[nc - kk];
+        xr = wki * a[j] - wkr * a[k];
+        a[j] = wkr * a[j] + wki * a[k];
+        a[k] = xr;
+    }
+    a[m] *= c[0];
+}
+
+
+void dstsub(int n, double *a, int nc, double *c)
+{
+    int j, k, kk, ks, m;
+    double wkr, wki, xr;
+    
+    m = n >> 1;
+    ks = nc / n;
+    kk = 0;
+    for (j = 1; j < m; j++) {
+        k = n - j;
+        kk += ks;
+        wkr = c[kk] - c[nc - kk];
+        wki = c[kk] + c[nc - kk];
+        xr = wki * a[k] - wkr * a[j];
+        a[k] = wkr * a[k] + wki * a[j];
+        a[j] = xr;
+    }
+    a[m] *= c[0];
+}
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fft4g.h	Fri May 01 19:26:11 2015 +0000
@@ -0,0 +1,1 @@
+void rdft(int, int, double *, int *, double *);

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main.cpp	Fri May 01 19:26:11 2015 +0000
@@ -0,0 +1,103 @@
+#include "mbed.h"
+#include "SLCD.h"
+#include "MAG3110.h"
+#include "fft4g.h"
+#include "aqm1248a_lcd.h"
+
+#define NMAX 256
+#define NMAXSQRT 32
+
+#define MAX(x,y) ((x) > (y) ? (x) : (y))
+
+MAG3110 mag(PTE25, PTE24);
+SLCD slcd;
+aqm1248a_lcd lcd;
+
+Ticker reader;
+
+bool modeFilling = true;
+int  nFilled = 0;
+double magBuffer[NMAX+1];
+
+void readerFunction() {
+    if (modeFilling) {
+        float x;
+        mag.getX(&x);
+        
+        if (nFilled < NMAX) {
+            magBuffer[nFilled++] = x;
+            if (nFilled >= NMAX) {
+                modeFilling = false;
+            }
+        }
+    }
+}
+
+
+void putdata(int n, double *a)
+{
+    int j;
+
+    double pi2 = 3.14159265*2 / n;
+    for (j = 0; j <n; j++) {
+        a[j] = sin(j*pi2*10)*10 + sin(j*pi2*15)*5 + sin(j*pi2*20)*10;
+    }
+}
+
+
+int main()
+{
+    char buf[80];
+    int n, ip[NMAXSQRT + 2];
+    double w[NMAX * 5 / 4];
+    ip[0] = 0;
+    n = NMAX;
+
+    int cnt = 0;
+    
+    lcd.setmode(NORMAL);
+    lcd.set_contrast(25);
+        
+    mag.enable();
+    
+    wait(0.1);
+    
+    reader.attach(&readerFunction, 0.0333333);
+    
+    while (1) {
+        while(modeFilling == true) wait(0.1);
+
+        rdft(n, 1, magBuffer, ip, w);
+
+        int n2 = n/2;
+        int height = lcd.height();
+        int width  = lcd.width();
+        
+        double max = 0;
+        for (int i = 0; i < n2; i++) {
+            int i2 = i*2;
+            magBuffer[i] = magBuffer[i2]*magBuffer[i2] + magBuffer[i2+1]*magBuffer[i2+1];
+            if (i > 0 && magBuffer[i] > max) max = magBuffer[i];
+        }
+        
+        lcd.cls();
+        
+        lcd.locate(0,0);
+        lcd.printf("%lf", max);
+        
+        max = height / max;
+        
+        for (int i = 1; i < n2; i++) {
+            lcd.line(i, height-1, i, height-1-max*magBuffer[i], 1);
+        }
+
+        sprintf(buf, "%4d", cnt++);           
+        slcd.printf(buf);
+        if (cnt > 9999) cnt = 0;
+        
+        nFilled = 0;
+        modeFilling = true;
+    }
+}
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/mbed.bld	Fri May 01 19:26:11 2015 +0000
@@ -0,0 +1,1 @@
+http://mbed.org/users/mbed_official/code/mbed/builds/8ab26030e058
\ No newline at end of file