/*============================================================================= // // This software has been released under the terms of the GNU General Public // license. See http://www.gnu.org/copyleft/gpl.html for details. // // Copyright 2001 Anders Johansson ajh@atri.curtin.edu.au // //============================================================================= */ /* Calculates a number of window functions. The following window functions are currently implemented: Boxcar, Triang, Hanning, Hamming, Blackman, Flattop and Kaiser. In the function call n is the number of filter taps and w the buffer in which the filter coefficients will be stored. */ #include <math.h> #include "dsp.h" /* // Boxcar // // n window length // w buffer for the window parameters */ void af_window_boxcar(int n, _ftype_t* w) { int i; // Calculate window coefficients for (i=0 ; i<n ; i++) w[i] = 1.0; } /* // Triang a.k.a Bartlett // // | (N-1)| // 2 * |k - -----| // | 2 | // w = 1.0 - --------------- // N+1 // n window length // w buffer for the window parameters */ void af_window_triang(int n, _ftype_t* w) { _ftype_t k1 = (_ftype_t)(n & 1); _ftype_t k2 = 1/((_ftype_t)n + k1); int end = (n + 1) >> 1; int i; // Calculate window coefficients for (i=0 ; i<end ; i++) w[i] = w[n-i-1] = (2.0*((_ftype_t)(i+1))-(1.0-k1))*k2; } /* // Hanning // 2*pi*k // w = 0.5 - 0.5*cos(------), where 0 < k <= N // N+1 // n window length // w buffer for the window parameters */ void af_window_hanning(int n, _ftype_t* w) { int i; _ftype_t k = 2*M_PI/((_ftype_t)(n+1)); // 2*pi/(N+1) // Calculate window coefficients for (i=0; i<n; i++) *w++ = 0.5*(1.0 - cos(k*(_ftype_t)(i+1))); } /* // Hamming // 2*pi*k // w(k) = 0.54 - 0.46*cos(------), where 0 <= k < N // N-1 // // n window length // w buffer for the window parameters */ void af_window_hamming(int n,_ftype_t* w) { int i; _ftype_t k = 2*M_PI/((_ftype_t)(n-1)); // 2*pi/(N-1) // Calculate window coefficients for (i=0; i<n; i++) *w++ = 0.54 - 0.46*cos(k*(_ftype_t)i); } /* // Blackman // 2*pi*k 4*pi*k // w(k) = 0.42 - 0.5*cos(------) + 0.08*cos(------), where 0 <= k < N // N-1 N-1 // // n window length // w buffer for the window parameters */ void af_window_blackman(int n,_ftype_t* w) { int i; _ftype_t k1 = 2*M_PI/((_ftype_t)(n-1)); // 2*pi/(N-1) _ftype_t k2 = 2*k1; // 4*pi/(N-1) // Calculate window coefficients for (i=0; i<n; i++) *w++ = 0.42 - 0.50*cos(k1*(_ftype_t)i) + 0.08*cos(k2*(_ftype_t)i); } /* // Flattop // 2*pi*k 4*pi*k // w(k) = 0.2810638602 - 0.5208971735*cos(------) + 0.1980389663*cos(------), where 0 <= k < N // N-1 N-1 // // n window length // w buffer for the window parameters */ void af_window_flattop(int n,_ftype_t* w) { int i; _ftype_t k1 = 2*M_PI/((_ftype_t)(n-1)); // 2*pi/(N-1) _ftype_t k2 = 2*k1; // 4*pi/(N-1) // Calculate window coefficients for (i=0; i<n; i++) *w++ = 0.2810638602 - 0.5208971735*cos(k1*(_ftype_t)i) + 0.1980389663*cos(k2*(_ftype_t)i); } /* Computes the 0th order modified Bessel function of the first kind. // (Needed to compute Kaiser window) // // y = sum( (x/(2*n))^2 ) // n */ #define BIZ_EPSILON 1E-21 // Max error acceptable static _ftype_t besselizero(_ftype_t x) { _ftype_t temp; _ftype_t sum = 1.0; _ftype_t u = 1.0; _ftype_t halfx = x/2.0; int n = 1; do { temp = halfx/(_ftype_t)n; u *=temp * temp; sum += u; n++; } while (u >= BIZ_EPSILON * sum); return(sum); } /* // Kaiser // // n window length // w buffer for the window parameters // b beta parameter of Kaiser window, Beta >= 1 // // Beta trades the rejection of the low pass filter against the // transition width from passband to stop band. Larger Beta means a // slower transition and greater stop band rejection. See Rabiner and // Gold (Theory and Application of DSP) under Kaiser windows for more // about Beta. The following table from Rabiner and Gold gives some // feel for the effect of Beta: // // All ripples in dB, width of transition band = D*N where N = window // length // // BETA D PB RIP SB RIP // 2.120 1.50 +-0.27 -30 // 3.384 2.23 0.0864 -40 // 4.538 2.93 0.0274 -50 // 5.658 3.62 0.00868 -60 // 6.764 4.32 0.00275 -70 // 7.865 5.0 0.000868 -80 // 8.960 5.7 0.000275 -90 // 10.056 6.4 0.000087 -100 */ void af_window_kaiser(int n, _ftype_t* w, _ftype_t b) { _ftype_t tmp; _ftype_t k1 = 1.0/besselizero(b); int k2 = 1 - (n & 1); int end = (n + 1) >> 1; int i; // Calculate window coefficients for (i=0 ; i<end ; i++){ tmp = (_ftype_t)(2*i + k2) / ((_ftype_t)n - 1.0); w[end-(1&(!k2))+i] = w[end-1-i] = k1 * besselizero(b*sqrt(1.0 - tmp*tmp)); } }