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/*=============================================================================
//
// This software has been released under the terms of the GNU 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 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 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 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 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 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 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
_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 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));
}
}
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