| /* |
| 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); |
| |
| 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); |
| } |
| } |
| |
| |
| 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]; |
| a[0] = a[m + mh]; |
| a[m + mh] = a[mh]; |
| m = mh; |
| } |
| a[1] = a[0]; |
| a[0] = 0; |
| bitrv1(n, a); |
| } |
| |
| |
| /* -------- child routines -------- */ |
| |
| |
| #include <math.h> |
| #ifndef M_PI_2 |
| #define M_PI_2 1.570796326794896619231321691639751442098584699687 |
| #endif |
| #ifndef WR5000 /* cos(M_PI_2*0.5000) */ |
| #define WR5000 0.707106781186547524400844362104849039284835937688 |
| #endif |
| #ifndef WR2500 /* cos(M_PI_2*0.2500) */ |
| #define WR2500 0.923879532511286756128183189396788286822416625863 |
| #endif |
| #ifndef WI2500 /* sin(M_PI_2*0.2500) */ |
| #define WI2500 0.382683432365089771728459984030398866761344562485 |
| #endif |
| |
| |
| #ifndef RDFT_LOOP_DIV /* control of the RDFT's speed & tolerance */ |
| #define RDFT_LOOP_DIV 64 |
| #endif |
| |
| #ifndef DCST_LOOP_DIV /* control of the DCT,DST's speed & tolerance */ |
| #define DCST_LOOP_DIV 64 |
| #endif |
| |
| |
| void bitrv2(int n, double *a) |
| { |
| int j0, k0, j1, k1, l, m, i, j, k; |
| double xr, xi, yr, yi; |
| |
| l = n >> 2; |
| m = 2; |
| while (m < l) { |
| l >>= 1; |
| m <<= 1; |
| } |
| if (m == l) { |
| j0 = 0; |
| for (k0 = 0; k0 < m; k0 += 2) { |
| k = k0; |
| for (j = j0; j < j0 + k0; j += 2) { |
| xr = a[j]; |
| xi = a[j + 1]; |
| yr = a[k]; |
| yi = a[k + 1]; |
| a[j] = yr; |
| a[j + 1] = yi; |
| a[k] = xr; |
| a[k + 1] = xi; |
| j1 = j + m; |
| k1 = k + 2 * m; |
| 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 += m; |
| k1 -= m; |
| 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 += m; |
| k1 += 2 * m; |
| 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; |
| for (i = n >> 1; i > (k ^= i); i >>= 1); |
| } |
| j1 = j0 + k0 + m; |
| k1 = j1 + m; |
| 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; |
| for (i = n >> 1; i > (j0 ^= i); i >>= 1); |
| } |
| } else { |
| j0 = 0; |
| for (k0 = 2; k0 < m; k0 += 2) { |
| for (i = n >> 1; i > (j0 ^= i); i >>= 1); |
| k = k0; |
| for (j = j0; j < j0 + k0; j += 2) { |
| xr = a[j]; |
| xi = a[j + 1]; |
| yr = a[k]; |
| yi = a[k + 1]; |
| a[j] = yr; |
| a[j + 1] = yi; |
| a[k] = xr; |
| a[k + 1] = xi; |
| j1 = j + m; |
| k1 = k + m; |
| 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; |
| for (i = n >> 1; i > (k ^= i); i >>= 1); |
| } |
| } |
| } |
| } |
| |
| |
| void bitrv2conj(int n, double *a) |
| { |
| int j0, k0, j1, k1, l, m, i, j, k; |
| double xr, xi, yr, yi; |
| |
| l = n >> 2; |
| m = 2; |
| while (m < l) { |
| l >>= 1; |
| m <<= 1; |
| } |
| if (m == l) { |
| j0 = 0; |
| for (k0 = 0; k0 < m; k0 += 2) { |
| k = k0; |
| for (j = j0; j < j0 + k0; j += 2) { |
| xr = a[j]; |
| xi = -a[j + 1]; |
| yr = a[k]; |
| yi = -a[k + 1]; |
| a[j] = yr; |
| a[j + 1] = yi; |
| a[k] = xr; |
| a[k + 1] = xi; |
| j1 = j + m; |
| k1 = k + 2 * m; |
| 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 += m; |
| k1 -= m; |
| 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 += m; |
| k1 += 2 * m; |
| 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; |
| for (i = n >> 1; i > (k ^= i); i >>= 1); |
| } |
| k1 = j0 + k0; |
| a[k1 + 1] = -a[k1 + 1]; |
| j1 = k1 + m; |
| k1 = j1 + m; |
| 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 += m; |
| a[k1 + 1] = -a[k1 + 1]; |
| for (i = n >> 1; i > (j0 ^= i); i >>= 1); |
| } |
| } else { |
| a[1] = -a[1]; |
| a[m + 1] = -a[m + 1]; |
| j0 = 0; |
| for (k0 = 2; k0 < m; k0 += 2) { |
| for (i = n >> 1; i > (j0 ^= i); i >>= 1); |
| k = k0; |
| for (j = j0; j < j0 + k0; j += 2) { |
| xr = a[j]; |
| xi = -a[j + 1]; |
| yr = a[k]; |
| yi = -a[k + 1]; |
| a[j] = yr; |
| a[j + 1] = yi; |
| a[k] = xr; |
| a[k + 1] = xi; |
| j1 = j + m; |
| k1 = k + m; |
| 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; |
| for (i = n >> 1; i > (k ^= i); i >>= 1); |
| } |
| k1 = j0 + k0; |
| a[k1 + 1] = -a[k1 + 1]; |
| a[k1 + m + 1] = -a[k1 + m + 1]; |
| } |
| } |
| } |
| |
| |
| void bitrv1(int n, double *a) |
| { |
| int j0, k0, j1, k1, l, m, i, j, k; |
| double x; |
| |
| l = n >> 2; |
| m = 1; |
| while (m < l) { |
| l >>= 1; |
| m <<= 1; |
| } |
| if (m == l) { |
| j0 = 0; |
| for (k0 = 0; k0 < m; k0++) { |
| k = k0; |
| for (j = j0; j < j0 + k0; j++) { |
| x = a[j]; |
| a[j] = a[k]; |
| a[k] = x; |
| j1 = j + m; |
| k1 = k + 2 * m; |
| x = a[j1]; |
| a[j1] = a[k1]; |
| a[k1] = x; |
| j1 += m; |
| k1 -= m; |
| x = a[j1]; |
| a[j1] = a[k1]; |
| a[k1] = x; |
| j1 += m; |
| k1 += 2 * m; |
| x = a[j1]; |
| a[j1] = a[k1]; |
| a[k1] = x; |
| for (i = n >> 1; i > (k ^= i); i >>= 1); |
| } |
| j1 = j0 + k0 + m; |
| k1 = j1 + m; |
| x = a[j1]; |
| a[j1] = a[k1]; |
| a[k1] = x; |
| for (i = n >> 1; i > (j0 ^= i); i >>= 1); |
| } |
| } else { |
| j0 = 0; |
| for (k0 = 1; k0 < m; k0++) { |
| for (i = n >> 1; i > (j0 ^= i); i >>= 1); |
| k = k0; |
| for (j = j0; j < j0 + k0; j++) { |
| x = a[j]; |
| a[j] = a[k]; |
| a[k] = x; |
| j1 = j + m; |
| k1 = k + m; |
| x = a[j1]; |
| a[j1] = a[k1]; |
| a[k1] = x; |
| for (i = n >> 1; i > (k ^= i); i >>= 1); |
| } |
| } |
| } |
| } |
| |
| |
| void cftfsub(int n, double *a) |
| { |
| void cft1st(int n, double *a); |
| void cftmdl(int n, int l, double *a); |
| int j, j1, j2, j3, l; |
| double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; |
| |
| l = 2; |
| if (n > 8) { |
| cft1st(n, a); |
| l = 8; |
| while ((l << 2) < n) { |
| cftmdl(n, l, a); |
| 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) |
| { |
| void cft1st(int n, double *a); |
| void cftmdl(int n, int l, double *a); |
| int j, j1, j2, j3, l; |
| double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; |
| |
| l = 2; |
| if (n > 8) { |
| cft1st(n, a); |
| l = 8; |
| while ((l << 2) < n) { |
| cftmdl(n, l, a); |
| 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) |
| { |
| int j, kj, kr; |
| double ew, wn4r, 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; |
| wn4r = WR5000; |
| 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] = wn4r * (x0r - x0i); |
| a[11] = wn4r * (x0r + x0i); |
| x0r = x3i + x1r; |
| x0i = x3r - x1i; |
| a[14] = wn4r * (x0i - x0r); |
| a[15] = wn4r * (x0i + x0r); |
| ew = M_PI_2 / n; |
| kr = 0; |
| for (j = 16; j < n; j += 16) { |
| for (kj = n >> 2; kj > (kr ^= kj); kj >>= 1); |
| wk1r = cos(ew * kr); |
| wk1i = sin(ew * kr); |
| wk2r = 1 - 2 * wk1i * wk1i; |
| wk2i = 2 * wk1i * wk1r; |
| 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; |
| x0r = wn4r * (wk1r - wk1i); |
| wk1i = wn4r * (wk1r + wk1i); |
| wk1r = x0r; |
| 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) |
| { |
| int j, j1, j2, j3, k, kj, kr, m, m2; |
| double ew, wn4r, 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; |
| } |
| wn4r = WR5000; |
| 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] = wn4r * (x0r - x0i); |
| a[j1 + 1] = wn4r * (x0r + x0i); |
| x0r = x3i + x1r; |
| x0i = x3r - x1i; |
| a[j3] = wn4r * (x0i - x0r); |
| a[j3 + 1] = wn4r * (x0i + x0r); |
| } |
| ew = M_PI_2 / n; |
| kr = 0; |
| m2 = 2 * m; |
| for (k = m2; k < n; k += m2) { |
| for (kj = n >> 2; kj > (kr ^= kj); kj >>= 1); |
| wk1r = cos(ew * kr); |
| wk1i = sin(ew * kr); |
| wk2r = 1 - 2 * wk1i * wk1i; |
| wk2i = 2 * wk1i * wk1r; |
| 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; |
| } |
| x0r = wn4r * (wk1r - wk1i); |
| wk1i = wn4r * (wk1r + wk1i); |
| wk1r = x0r; |
| 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 i, i0, j, k; |
| double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi; |
| |
| ec = 2 * M_PI_2 / n; |
| wkr = 0; |
| wki = 0; |
| wdi = cos(ec); |
| wdr = sin(ec); |
| wdi *= wdr; |
| wdr *= wdr; |
| w1r = 1 - 2 * wdr; |
| w1i = 2 * wdi; |
| ss = 2 * w1i; |
| i = n >> 1; |
| for (;;) { |
| i0 = i - 4 * RDFT_LOOP_DIV; |
| if (i0 < 4) { |
| i0 = 4; |
| } |
| for (j = i - 4; j >= i0; j -= 4) { |
| k = n - j; |
| xr = a[j + 2] - a[k - 2]; |
| xi = a[j + 3] + a[k - 1]; |
| yr = wdr * xr - wdi * xi; |
| yi = wdr * xi + wdi * xr; |
| a[j + 2] -= yr; |
| a[j + 3] -= yi; |
| a[k - 2] += yr; |
| a[k - 1] -= yi; |
| wkr += ss * wdi; |
| wki += ss * (0.5 - wdr); |
| 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; |
| wdr += ss * wki; |
| wdi += ss * (0.5 - wkr); |
| } |
| if (i0 == 4) { |
| break; |
| } |
| wkr = 0.5 * sin(ec * i0); |
| wki = 0.5 * cos(ec * i0); |
| wdr = 0.5 - (wkr * w1r - wki * w1i); |
| wdi = wkr * w1i + wki * w1r; |
| wkr = 0.5 - wkr; |
| i = i0; |
| } |
| xr = a[2] - a[n - 2]; |
| xi = a[3] + a[n - 1]; |
| yr = wdr * xr - wdi * xi; |
| yi = wdr * xi + wdi * xr; |
| a[2] -= yr; |
| a[3] -= yi; |
| a[n - 2] += yr; |
| a[n - 1] -= yi; |
| } |
| |
| |
| void rftbsub(int n, double *a) |
| { |
| int i, i0, j, k; |
| double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi; |
| |
| ec = 2 * M_PI_2 / n; |
| wkr = 0; |
| wki = 0; |
| wdi = cos(ec); |
| wdr = sin(ec); |
| wdi *= wdr; |
| wdr *= wdr; |
| w1r = 1 - 2 * wdr; |
| w1i = 2 * wdi; |
| ss = 2 * w1i; |
| i = n >> 1; |
| a[i + 1] = -a[i + 1]; |
| for (;;) { |
| i0 = i - 4 * RDFT_LOOP_DIV; |
| if (i0 < 4) { |
| i0 = 4; |
| } |
| for (j = i - 4; j >= i0; j -= 4) { |
| k = n - j; |
| xr = a[j + 2] - a[k - 2]; |
| xi = a[j + 3] + a[k - 1]; |
| yr = wdr * xr + wdi * xi; |
| yi = wdr * xi - wdi * xr; |
| a[j + 2] -= yr; |
| a[j + 3] = yi - a[j + 3]; |
| a[k - 2] += yr; |
| a[k - 1] = yi - a[k - 1]; |
| wkr += ss * wdi; |
| wki += ss * (0.5 - wdr); |
| 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]; |
| wdr += ss * wki; |
| wdi += ss * (0.5 - wkr); |
| } |
| if (i0 == 4) { |
| break; |
| } |
| wkr = 0.5 * sin(ec * i0); |
| wki = 0.5 * cos(ec * i0); |
| wdr = 0.5 - (wkr * w1r - wki * w1i); |
| wdi = wkr * w1i + wki * w1r; |
| wkr = 0.5 - wkr; |
| i = i0; |
| } |
| xr = a[2] - a[n - 2]; |
| xi = a[3] + a[n - 1]; |
| yr = wdr * xr + wdi * xi; |
| yi = wdr * xi - wdi * xr; |
| a[2] -= yr; |
| a[3] = yi - a[3]; |
| a[n - 2] += yr; |
| a[n - 1] = yi - a[n - 1]; |
| a[1] = -a[1]; |
| } |
| |
| |
| void dctsub(int n, double *a) |
| { |
| int i, i0, j, k, m; |
| double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi; |
| |
| ec = M_PI_2 / n; |
| wkr = 0.5; |
| wki = 0.5; |
| w1r = cos(ec); |
| w1i = sin(ec); |
| wdr = 0.5 * (w1r - w1i); |
| wdi = 0.5 * (w1r + w1i); |
| ss = 2 * w1i; |
| m = n >> 1; |
| i = 0; |
| for (;;) { |
| i0 = i + 2 * DCST_LOOP_DIV; |
| if (i0 > m - 2) { |
| i0 = m - 2; |
| } |
| for (j = i + 2; j <= i0; j += 2) { |
| k = n - j; |
| xr = wdi * a[j - 1] - wdr * a[k + 1]; |
| xi = wdr * a[j - 1] + wdi * a[k + 1]; |
| wkr -= ss * wdi; |
| wki += ss * wdr; |
| yr = wki * a[j] - wkr * a[k]; |
| yi = wkr * a[j] + wki * a[k]; |
| wdr -= ss * wki; |
| wdi += ss * wkr; |
| a[k + 1] = xr; |
| a[k] = yr; |
| a[j - 1] = xi; |
| a[j] = yi; |
| } |
| if (i0 == m - 2) { |
| break; |
| } |
| wdr = cos(ec * i0); |
| wdi = sin(ec * i0); |
| wkr = 0.5 * (wdr - wdi); |
| wki = 0.5 * (wdr + wdi); |
| wdr = wkr * w1r - wki * w1i; |
| wdi = wkr * w1i + wki * w1r; |
| i = i0; |
| } |
| xr = wdi * a[m - 1] - wdr * a[m + 1]; |
| a[m - 1] = wdr * a[m - 1] + wdi * a[m + 1]; |
| a[m + 1] = xr; |
| a[m] *= wki + ss * wdr; |
| } |
| |
| |
| void dstsub(int n, double *a) |
| { |
| int i, i0, j, k, m; |
| double ec, w1r, w1i, wkr, wki, wdr, wdi, ss, xr, xi, yr, yi; |
| |
| ec = M_PI_2 / n; |
| wkr = 0.5; |
| wki = 0.5; |
| w1r = cos(ec); |
| w1i = sin(ec); |
| wdr = 0.5 * (w1r - w1i); |
| wdi = 0.5 * (w1r + w1i); |
| ss = 2 * w1i; |
| m = n >> 1; |
| i = 0; |
| for (;;) { |
| i0 = i + 2 * DCST_LOOP_DIV; |
| if (i0 > m - 2) { |
| i0 = m - 2; |
| } |
| for (j = i + 2; j <= i0; j += 2) { |
| k = n - j; |
| xr = wdi * a[k + 1] - wdr * a[j - 1]; |
| xi = wdr * a[k + 1] + wdi * a[j - 1]; |
| wkr -= ss * wdi; |
| wki += ss * wdr; |
| yr = wki * a[k] - wkr * a[j]; |
| yi = wkr * a[k] + wki * a[j]; |
| wdr -= ss * wki; |
| wdi += ss * wkr; |
| a[j - 1] = xr; |
| a[j] = yr; |
| a[k + 1] = xi; |
| a[k] = yi; |
| } |
| if (i0 == m - 2) { |
| break; |
| } |
| wdr = cos(ec * i0); |
| wdi = sin(ec * i0); |
| wkr = 0.5 * (wdr - wdi); |
| wki = 0.5 * (wdr + wdi); |
| wdr = wkr * w1r - wki * w1i; |
| wdi = wkr * w1i + wki * w1r; |
| i = i0; |
| } |
| xr = wdi * a[m + 1] - wdr * a[m - 1]; |
| a[m + 1] = wdr * a[m + 1] + wdi * a[m - 1]; |
| a[m - 1] = xr; |
| a[m] *= wki + ss * wdr; |
| } |
| |
| |
| void dctsub4(int n, double *a) |
| { |
| int m; |
| double wki, wdr, wdi, xr; |
| |
| wki = WR5000; |
| m = n >> 1; |
| if (m == 2) { |
| wdr = wki * WI2500; |
| wdi = wki * WR2500; |
| xr = wdi * a[1] - wdr * a[3]; |
| a[1] = wdr * a[1] + wdi * a[3]; |
| a[3] = xr; |
| } |
| a[m] *= wki; |
| } |
| |
| |
| void dstsub4(int n, double *a) |
| { |
| int m; |
| double wki, wdr, wdi, xr; |
| |
| wki = WR5000; |
| m = n >> 1; |
| if (m == 2) { |
| wdr = wki * WI2500; |
| wdi = wki * WR2500; |
| xr = wdi * a[3] - wdr * a[1]; |
| a[3] = wdr * a[3] + wdi * a[1]; |
| a[1] = xr; |
| } |
| a[m] *= wki; |
| } |
| |
