scummvm/sound/resample.cpp

/*
* July 5, 1991
* Copyright 1991 Lance Norskog And Sundry Contributors
* This source code is freely redistributable and may be used for
* any purpose.	 This copyright notice must be maintained. 
* Lance Norskog And Sundry Contributors are not responsible for 
* the consequences of using this software.
*/

/*
 * Sound Tools rate change effect file.
 * Spiffy rate changer using Smith & Wesson Bandwidth-Limited Interpolation.
 * The algorithm is described in "Bandlimited Interpolation -
 * Introduction and Algorithm" by Julian O. Smith III.
 * Available on ccrma-ftp.stanford.edu as
 * pub/BandlimitedInterpolation.eps.Z or similar.
 *
 * The latest stand alone version of this algorithm can be found
 * at ftp://ccrma-ftp.stanford.edu/pub/NeXT/
 * under the name of resample-version.number.tar.Z
 *
 * NOTE: There is a newer version of the resample routine then what
 * this file was originally based on.  Those adventurous might be
 * interested in reviewing its improvesments and porting it to this
 * version.
 */

/* Fixed bug: roll off frequency was wrong, too high by 2 when upsampling,
 * too low by 2 when downsampling.
 * Andreas Wilde, 12. Feb. 1999, andreas@eakaw2.et.tu-dresden.de
*/

/*
 * October 29, 1999
 * Various changes, bugfixes(?), increased precision, by Stan Brooks.
 *
 * This source code is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 *
 */ 
/*
 * SJB: [11/25/99]
 * TODO: another idea for improvement...
 * note that upsampling usually doesn't require interpolation,
 * therefore is faster and more accurate than downsampling.
 * Downsampling by an integer factor is also simple, since
 * it just involves decimation if the input is already 
 * lowpass-filtered to the output Nyquist freqency.
 * Get the idea? :)
 */

#include <math.h>
#include <stdlib.h>
#include <string.h>
#include "rate.h"

/* resample includes */
#include "resample.h"

/* this Float MUST match that in filter.c */
#define Float double/*float*/

/* largest factor for which exact-coefficients upsampling will be used */
#define NQMAX 511

#define BUFFSIZE 8192 /*16384*/	 /* Total I/O buffer size */

/* Private data for Lerp via LCM file */
typedef struct resamplestuff {
	double Factor;     /* Factor = Fout/Fin sample rates */
	double rolloff;    /* roll-off frequency */
	double beta;	      /* passband/stopband tuning magic */
	int quadr;	      /* non-zero to use qprodUD quadratic interpolation */
	long Nmult;
	long Nwing;
	long Nq;
	Float *Imp;	      /* impulse [Nwing+1] Filter coefficients */

	double Time;	      /* Current time/pos in input sample */
	long dhb;

	long a, b;	      /* gcd-reduced input,output rates	  */
	long t;	      /* Current time/pos for exact-coeff's method */

	long Xh;	      /* number of past/future samples needed by filter	 */
	long Xoff;	      /* Xh plus some room for creep  */
	long Xread;	      /* X[Xread] is start-position to enter new samples */
	long Xp;	      /* X[Xp] is position to start filter application	 */
	long Xsize, Ysize;  /* size (Floats) of X[],Y[]	  */
	long Yposition;		/* FIXME: offset into Y buffer */
	Float *X, *Y;      /* I/O buffers */
} *resample_t;

static void LpFilter(double c[],
                     long N,
                     double frq,
                     double Beta,
                     long Num);

/* makeFilter is used by filter.c */
int makeFilter(Float Imp[],
               long Nwing,
               double Froll,
               double Beta,
               long Num,
               int Normalize);

static long SrcUD(resample_t r, long Nx);
static long SrcEX(resample_t r, long Nx);


/*
 * Process options
 */
int st_resample_getopts(eff_t effp, int n, char **argv) {
	resample_t r = (resample_t) effp->priv;

	/* These defaults are conservative with respect to aliasing. */
	r->rolloff = 0.80;
	r->beta = 16; /* anything <=2 means Nutall window */
	r->quadr = 0;
	r->Nmult = 45;

	/* This used to fail, but with sox-12.15 it works. AW */
	if ((n >= 1)) {
		if (!strcmp(argv[0], "-qs")) {
			r->quadr = 1;
			n--;
			argv++;
		} else if (!strcmp(argv[0], "-q")) {
			r->rolloff = 0.875;
			r->quadr = 1;
			r->Nmult = 75;
			n--;
			argv++;
		} else if (!strcmp(argv[0], "-ql")) {
			r->rolloff = 0.94;
			r->quadr = 1;
			r->Nmult = 149;
			n--;
			argv++;
		}
	}

	if ((n >= 1) && (sscanf(argv[0], "%lf", &r->rolloff) != 1)) {
		st_fail("Usage: resample [ rolloff [ beta ] ]");
		return (ST_EOF);
	} else if ((r->rolloff <= 0.01) || (r->rolloff >= 1.0)) {
		st_fail("resample: rolloff factor (%f) no good, should be 0.01<x<1.0", r->rolloff);
		return (ST_EOF);
	}

	if ((n >= 2) && !sscanf(argv[1], "%lf", &r->beta)) {
		st_fail("Usage: resample [ rolloff [ beta ] ]");
		return (ST_EOF);
	} else if (r->beta <= 2.0) {
		r->beta = 0;
		st_report("resample opts: Nuttall window, cutoff %f\n", r->rolloff);
	} else {
		st_report("resample opts: Kaiser window, cutoff %f, beta %f\n", r->rolloff, r->beta);
	}
	return (ST_SUCCESS);
}

/*
 * Prepare processing.
 */
int st_resample_start(eff_t effp, st_rate_t inrate, st_rate_t outrate) {
	resample_t r = (resample_t) effp->priv;
	long Xoff, gcdrate;
	int i;

	if (inrate == outrate) {
		st_fail("Input and Output rates must be different to use resample effect");
		return (ST_EOF);
	}

	r->Factor = (double)outrate / (double)inrate;

	gcdrate = st_gcd(inrate, outrate);
	r->a = inrate / gcdrate;
	r->b = outrate / gcdrate;

	if (r->a <= r->b && r->b <= NQMAX) {
		r->quadr = -1; /* exact coeff's	  */
		r->Nq = r->b;  /* MAX(r->a,r->b);	*/
	} else {
		r->Nq = Nc; /* for now */
	}

	/* Check for illegal constants */
# if 0
	if (Lp >= 16)
		st_fail("Error: Lp>=16");
	if (Nb + Nhg + NLpScl >= 32)
		st_fail("Error: Nb+Nhg+NLpScl>=32");
	if (Nh + Nb > 32)
		st_fail("Error: Nh+Nb>32");
# endif

	/* Nwing: # of filter coeffs in right wing */
	r->Nwing = r->Nq * (r->Nmult / 2 + 1) + 1;

	r->Imp = (Float *)malloc(sizeof(Float) * (r->Nwing + 2)) + 1;
	/* need Imp[-1] and Imp[Nwing] for quadratic interpolation */
	/* returns error # <=0, or adjusted wing-len > 0 */
	i = makeFilter(r->Imp, r->Nwing, r->rolloff, r->beta, r->Nq, 1);
	if (i <= 0) {
		st_fail("resample: Unable to make filter\n");
		return (ST_EOF);
	}

	st_report("Nmult: %ld, Nwing: %ld, Nq: %ld\n",r->Nmult,r->Nwing,r->Nq);	// FIXME

	if (r->quadr < 0) { /* exact coeff's method */
		r->Xh = r->Nwing / r->b;
		st_report("resample: rate ratio %ld:%ld, coeff interpolation not needed\n", r->a, r->b);
	} else {
		r->dhb = Np;	/* Fixed-point Filter sampling-time-increment */
		if (r->Factor < 1.0)
			r->dhb = (long)(r->Factor * Np + 0.5);
		r->Xh = (r->Nwing << La) / r->dhb;
		/* (Xh * dhb)>>La is max index into Imp[] */
	}

	/* reach of LP filter wings + some creeping room */
	Xoff = r->Xh + 10;
	r->Xoff = Xoff;

	/* Current "now"-sample pointer for input to filter */
	r->Xp = Xoff;
	/* Position in input array to read into */
	r->Xread = Xoff;
	/* Current-time pointer for converter */
	r->Time = Xoff;
	if (r->quadr < 0) { /* exact coeff's method */
		r->t = Xoff * r->Nq;
	}
	i = BUFFSIZE - 2 * Xoff;
	if (i < r->Factor + 1.0 / r->Factor)	/* Check input buffer size */
	{
		st_fail("Factor is too small or large for BUFFSIZE");
		return (ST_EOF);
	}

	r->Xsize = (long)(2 * Xoff + i / (1.0 + r->Factor));
	r->Ysize = BUFFSIZE - r->Xsize;
	st_report("Xsize %ld, Ysize %ld, Xoff %ld",r->Xsize,r->Ysize,r->Xoff);	// FIXME

	r->X = (Float *) malloc(sizeof(Float) * (BUFFSIZE));
	r->Y = r->X + r->Xsize;
	r->Yposition = 0;

	/* Need Xoff zeros at beginning of sample */
	for (i = 0; i < Xoff; i++)
		r->X[i] = 0;
	return (ST_SUCCESS);
}

/*
 * Processed signed long samples from ibuf to obuf.
 * Return number of samples processed.
 */
int st_resample_flow(eff_t effp, InputStream &input, st_sample_t *obuf, st_size_t *osamp) {
	resample_t r = (resample_t) effp->priv;
	long i, k, last;
	long Nout;		// The number of bytes we effectively output
	long Nx;		// The number of bytes we will read from input
	long Nproc;		// The number of bytes we process to generate Nout output bytes

#if 1	// FIXME: Hack to generate stereo output
	*osamp >>= 1;
#endif

	/* constrain amount we actually process */
	fprintf(stderr,"Xp %d, Xread %d\n",r->Xp, r->Xread);

	// Initially assume we process the full X buffer starting at the filter
	// start position.
	Nproc = r->Xsize - r->Xp;
printf("FOO(1) Nproc %ld\n", Nproc);

	// Nproc is bounded indirectly by the size of output buffer, and also by
	// the remaining size of the Y buffer (whichever is smaller).
	i = MIN(r->Ysize - r->Yposition, (long)*osamp);
	if (Nproc * r->Factor >= i)
		Nproc = (long)(i / r->Factor);

printf("FOO(2) Nproc %ld\n", Nproc);

	// Now that we know how many bytes we want to process, we determine
	// how many bytes to read. We already have Xread bytes in our input
	// buffer, so we need Nproc - r->Xread more bytes.
	Nx = Nproc - r->Xread + r->Xoff + r->Xp; // FIXME: Fingolfing thinks this is the correct thing, not what's in the next line!
//	Nx = Nproc - r->Xread; /* space for right-wing future-data */
	if (Nx <= 0) {
		st_fail("resample: Can not handle this sample rate change. Nx not positive: %d", Nx);
		return (ST_EOF);
	}
	
	// Nx is the number of bytes we'd like to read, but of course that is limited
	// by the number of bytes actually available...
	if (Nx > (long)input.size())
		Nx = (long)input.size();
	fprintf(stderr,"Nx %d\n",Nx);

	// Read in Nx bytes
	for (i = r->Xread; i < Nx + r->Xread ; i++)
		r->X[i] = (Float)input.read();

	last = Nx + r->Xread;	// 'last' is the idx after the last valid byte in X (i.e. number of bytes are in buffer X right now)
	
	// Finally compute the effective number of bytes to process
	Nproc = last - r->Xoff - r->Xp;
printf("FOO(3) Nproc %ld\n", Nproc);

	if (Nproc <= 0) {
		/* fill in starting here next time */
		r->Xread = last;
		/* leave *isamp alone, we consumed it */
		*osamp = 0;
		return (ST_SUCCESS);
	}
	if (r->quadr < 0) { /* exact coeff's method */
		long creep;
		Nout = SrcEX(r, Nproc);
		fprintf(stderr,"Nproc %d --> %d\n",Nproc,Nout);
		/* Move converter Nproc samples back in time */
		r->t -= Nproc * r->b;
		/* Advance by number of samples processed */
		r->Xp += Nproc;
		/* Calc time accumulation in Time */
		creep = r->t / r->b - r->Xoff;
		if (creep) {
			r->t -= creep * r->b;	 /* Remove time accumulation   */
			r->Xp += creep;	 /* and add it to read pointer */
			fprintf(stderr,"Nproc %ld, creep %ld\n",Nproc,creep);
		}
	} else { /* approx coeff's method */
		long creep;
		Nout = SrcUD(r, Nproc);
		fprintf(stderr,"Nproc %d --> %d\n",Nproc,Nout);
		/* Move converter Nproc samples back in time */
		r->Time -= Nproc;
		/* Advance by number of samples processed */
		r->Xp += Nproc;
		/* Calc time accumulation in Time */
		creep = (long)(r->Time - r->Xoff);
		if (creep) {
			r->Time -= creep;   /* Remove time accumulation   */
			r->Xp += creep;     /* and add it to read pointer */
			fprintf(stderr,"Nproc %ld, creep %ld\n",Nproc,creep);
		}
	}

	/* Copy back portion of input signal that must be re-used */
	k = r->Xp - r->Xoff;
	fprintf(stderr,"k %d, last %d\n",k,last);
	for (i = 0; i < last - k; i++)
		r->X[i] = r->X[i + k];

	/* Pos in input buff to read new data into */
	r->Xread = i;
	r->Xp = r->Xoff;

printf("osamp = %d, Nout = %ld\n", *osamp, Nout);
	for (i = 0; i < Nout; i++) {
		clampedAdd(*obuf++, (int)r->Y[i]);
#if 1	// FIXME: Hack to generate stereo output
		clampedAdd(*obuf++, (int)r->Y[i]);
#endif
	}

	// At this point, we used *osamp bytes out of Nout available bytes in the Y buffer.
	// If there are any bytes remaining, shift them to the start of the buffer,
	// and update Yposition


	*osamp = Nout;

	return (ST_SUCCESS);
}

/*
 * Process tail of input samples.
 */
int st_resample_drain(eff_t effp, st_sample_t *obuf, st_size_t *osamp) {
	resample_t r = (resample_t) effp->priv;
	long isamp_res, osamp_res;
	st_sample_t *Obuf;
	int rc;

	/*fprintf(stderr,"Xoff %d, Xt %d  <--- DRAIN\n",r->Xoff, r->Xt);*/

	/* stuff end with Xoff zeros */
	isamp_res = r->Xoff;
	osamp_res = *osamp;
	Obuf = obuf;
	while (isamp_res > 0 && osamp_res > 0) {
		st_sample_t Osamp;
		Osamp = osamp_res;
		ZeroInputStream zero(isamp_res);
		rc = st_resample_flow(effp, zero, Obuf, (st_size_t *) & Osamp);
		if (rc)
			return rc;
		/*fprintf(stderr,"DRAIN isamp,osamp	(%d,%d) -> (%d,%d)\n",
		    isamp_res,osamp_res,Isamp,Osamp);*/
		Obuf += Osamp;
		osamp_res -= Osamp;
		isamp_res = zero.size();
	}
	*osamp -= osamp_res;
	fprintf(stderr,"DRAIN osamp %d\n", *osamp);
	if (isamp_res)
		st_warn("drain overran obuf by %d\n", isamp_res);
	fflush(stderr);
	return (ST_SUCCESS);
}

/*
 * Do anything required when you stop reading samples.	
 * Don't close input file! 
 */
int st_resample_stop(eff_t effp) {
	resample_t r = (resample_t) effp->priv;

	free(r->Imp - 1);
	free(r->X);
	/* free(r->Y); Y is in same block starting at X */
	return (ST_SUCCESS);
}

/* over 90% of CPU time spent in this iprodUD() function */
/* quadratic interpolation */
static double qprodUD(const Float Imp[], const Float *Xp, long Inc, double T0,
                      long dhb, long ct) {
	const double f = 1.0 / (1 << La);
	double v;
	long Ho;

	Ho = (long)(T0 * dhb);
	Ho += (ct - 1) * dhb; /* so Float sum starts with smallest coef's */
	Xp += (ct - 1) * Inc;
	v = 0;
	do {
		Float coef;
		long Hoh;
		Hoh = Ho >> La;
		coef = Imp[Hoh];
		{
			Float dm, dp, t;
			dm = coef - Imp[Hoh - 1];
			dp = Imp[Hoh + 1] - coef;
			t = (Ho & Amask) * f;
			coef += ((dp - dm) * t + (dp + dm)) * t * 0.5;
		}
		/* filter coef, lower La bits by quadratic interpolation */
		v += coef * *Xp;   /* sum coeff * input sample */
		Xp -= Inc;	   /* Input signal step. NO CHECK ON ARRAY BOUNDS */
		Ho -= dhb;	   /* IR step */
	} while (--ct);
	return v;
}

/* linear interpolation */
static double iprodUD(const Float Imp[], const Float *Xp, long Inc,
                      double T0, long dhb, long ct) {
	const double f = 1.0 / (1 << La);
	double v;
	long Ho;

	Ho = (long)(T0 * dhb);
	Ho += (ct - 1) * dhb; /* so Float sum starts with smallest coef's */
	Xp += (ct - 1) * Inc;
	v = 0;
	do {
		Float coef;
		long Hoh;
		Hoh = Ho >> La;
		/* if (Hoh >= End) break; */
		coef = Imp[Hoh] + (Imp[Hoh + 1] - Imp[Hoh]) * (Ho & Amask) * f;
		/* filter coef, lower La bits by linear interpolation */
		v += coef * *Xp;   /* sum coeff * input sample */
		Xp -= Inc;	   /* Input signal step. NO CHECK ON ARRAY BOUNDS */
		Ho -= dhb;	   /* IR step */
	} while (--ct);
	return v;
}

/* From resample:filters.c */
/* Sampling rate conversion subroutine */

static long SrcUD(resample_t r, long Nx) {
	Float *Ystart, *Y;
	double Factor;
	double dt;		       /* Step through input signal */
	double time;
	double (*prodUD)(const Float Imp[], const Float *Xp, long Inc, double T0, long dhb, long ct);
	int n;

	prodUD = (r->quadr) ? qprodUD : iprodUD; /* quadratic or linear interp */
	Factor = r->Factor;
	time = r->Time;
	dt = 1.0 / Factor;	   /* Output sampling period */
	fprintf(stderr,"Factor %f, dt %f, ",Factor,dt);
	fprintf(stderr,"Time %f, ",r->Time);
	/* (Xh * dhb)>>La is max index into Imp[] */
	/*fprintf(stderr,"ct=%d\n",ct);*/
	fprintf(stderr,"ct=%.2f %d\n",(double)r->Nwing*Na/r->dhb, r->Xh);
	fprintf(stderr,"ct=%ld, T=%.6f, dhb=%6f, dt=%.6f\n", r->Xh, time-floor(time),(double)r->dhb/Na,dt);
	Ystart = Y = r->Y + r->Yposition;
	n = (int)ceil((double)Nx / dt);
	while (n--) {
		Float *Xp;
		double v;
		double T;
		T = time - floor(time);	   /* fractional part of Time */
		Xp = r->X + (long)time;	   /* Ptr to current input sample */

		/* Past  inner product: */
		v = (*prodUD)(r->Imp, Xp, -1, T, r->dhb, r->Xh); /* needs Np*Nmult in 31 bits */
		/* Future inner product: */
		v += (*prodUD)(r->Imp, Xp + 1, 1, (1.0 - T), r->dhb, r->Xh); /* prefer even total */

		if (Factor < 1)
			v *= Factor;
		*Y++ = v;		     /* Deposit output */
		time += dt;	     /* Move to next sample by time increment */
	}
	r->Time = time;
	fprintf(stderr,"Time %f\n",r->Time);
	return (Y - Ystart);	       /* Return the number of output samples */
}

/* exact coeff's */
static double prodEX(const Float Imp[], const Float *Xp,
                     long Inc, long T0, long dhb, long ct) {
	double v;
	const Float *Cp;

	Cp = Imp + (ct - 1) * dhb + T0; /* so Float sum starts with smallest coef's */
	Xp += (ct - 1) * Inc;
	v = 0;
	do {
		v += *Cp * *Xp;   /* sum coeff * input sample */
		Cp -= dhb;	   /* IR step */
		Xp -= Inc;	   /* Input signal step. */
	} while (--ct);
	return v;
}

static long SrcEX(resample_t r, long Nx) {
	Float *Ystart, *Y;
	double Factor;
	long a, b;
	long time;
	int n;

	Factor = r->Factor;
	time = r->t;
	a = r->a;
	b = r->b;
	Ystart = Y = r->Y + r->Yposition;
	n = (Nx * b + (a - 1)) / a;
	while (n--) {
		Float *Xp;
		double v;
		long T;
		T = time % b;		   /* fractional part of Time */
		Xp = r->X + (time / b);	   /* Ptr to current input sample */

		/* Past	 inner product: */
		v = prodEX(r->Imp, Xp, -1, T, b, r->Xh);
		/* Future inner product: */
		v += prodEX(r->Imp, Xp + 1, 1, b - T, b, r->Xh);

		if (Factor < 1)
			v *= Factor;
		*Y++ = v;	      /* Deposit output */
		time += a;	      /* Move to next sample by time increment */
	}
	r->t = time;
	return (Y - Ystart);	       /* Return the number of output samples */
}

int makeFilter(Float Imp[], long Nwing, double Froll, double Beta,
               long Num, int Normalize) {
	double *ImpR;
	long Mwing, i;

	if (Nwing > MAXNWING)		      /* Check for valid parameters */
		return ( -1);
	if ((Froll <= 0) || (Froll > 1))
		return ( -2);

	/* it does help accuracy a bit to have the window stop at
	 * a zero-crossing of the sinc function */
	Mwing = (long)(floor((double)Nwing / (Num / Froll)) * (Num / Froll) + 0.5);
	if (Mwing == 0)
		return ( -4);

	ImpR = (double *) malloc(sizeof(double) * Mwing);

	/* Design a Nuttall or Kaiser windowed Sinc low-pass filter */
	LpFilter(ImpR, Mwing, Froll, Beta, Num);

	if (Normalize) { /* 'correct' the DC gain of the lowpass filter */
		long Dh;
		double DCgain;
		DCgain = 0;
		Dh = Num;			 /* Filter sampling period for factors>=1 */
		for (i = Dh; i < Mwing; i += Dh)
			DCgain += ImpR[i];
		DCgain = 2 * DCgain + ImpR[0];    /* DC gain of real coefficients */
		st_report("DCgain err=%.12f",DCgain-1.0);	// FIXME

		DCgain = 1.0 / DCgain;
		for (i = 0; i < Mwing; i++)
			Imp[i] = ImpR[i] * DCgain;

	} else {
		for (i = 0; i < Mwing; i++)
			Imp[i] = ImpR[i];
	}
	free(ImpR);
	for (i = Mwing; i <= Nwing; i++)
		Imp[i] = 0;
	/* Imp[Mwing] and Imp[-1] needed for quadratic interpolation */
	Imp[ -1] = Imp[1];

	return (Mwing);
}

/* LpFilter()
 *
 * reference: "Digital Filters, 2nd edition"
 *	      R.W. Hamming, pp. 178-179
 *
 * Izero() computes the 0th order modified bessel function of the first kind.
 *    (Needed to compute Kaiser window).
 *
 * LpFilter() computes the coeffs of a Kaiser-windowed low pass filter with
 *    the following characteristics:
 *
 *	 c[]  = array in which to store computed coeffs
 *	 frq  = roll-off frequency of filter
 *	 N    = Half the window length in number of coeffs
 *	 Beta = parameter of Kaiser window
 *	 Num  = number of coeffs before 1/frq
 *
 * Beta trades the rejection of the lowpass filter against the transition
 *    width from passband to stopband.	Larger Beta means a slower
 *    transition and greater stopband 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
 */


#define IzeroEPSILON 1E-21		 /* Max error acceptable in Izero */

static double Izero(double x) {
	double sum, u, halfx, temp;
	long n;

	sum = u = n = 1;
	halfx = x / 2.0;
	do {
		temp = halfx / (double)n;
		n += 1;
		temp *= temp;
		u *= temp;
		sum += u;
	} while (u >= IzeroEPSILON*sum);
	return (sum);
}

static void LpFilter(double *c, long N, double frq, double Beta, long Num) {
	long i;

	/* Calculate filter coeffs: */
	c[0] = frq;
	for (i = 1; i < N; i++) {
		double x = M_PI * (double)i / (double)(Num);
		c[i] = sin(x * frq) / x;
	}

	if (Beta > 2) { /* Apply Kaiser window to filter coeffs: */
		double IBeta = 1.0 / Izero(Beta);
		for (i = 1; i < N; i++) {
			double x = (double)i / (double)(N);
			c[i] *= Izero(Beta * sqrt(1.0 - x * x)) * IBeta;
		}
	} else { /* Apply Nuttall window: */
		for (i = 0; i < N; i++) {
			double x = M_PI * i / N;
			c[i] *= 0.36335819 + 0.4891775 * cos(x) + 0.1365995 * cos(2 * x) + 0.0106411 * cos(3 * x);
		}
	}
}