ref: 9228e6c128882dcb8bbd5a855eb7fb8a1a22d2a3
dir: /src/resample.c/
/*
* libSoX 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
*
*
* FILE: resample.h
* BY: Julius Smith (at CCRMA, Stanford U)
* C BY: translated from SAIL to C by Christopher Lee Fraley
* (cf0v@andrew.cmu.edu)
* DATE: 7-JUN-88
* VERS: 2.0 (17-JUN-88, 3:00pm)
*
* 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.
*
* 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.
*
* 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.
*/
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include "sox_i.h"
/* Conversion constants */
#define Lc 7
#define Nc (1<<Lc)
#define La 16
#define Na (1<<La)
#define Lp (Lc+La)
#define Np (1<<Lp)
#define Amask (Na-1)
#define Pmask (Np-1)
#define MAXNWING (80<<Lc)
/* Description of constants:
*
* Nc - is the number of look-up values available for the lowpass filter
* between the beginning of its impulse response and the "cutoff time"
* of the filter. The cutoff time is defined as the reciprocal of the
* lowpass-filter cut off frequence in Hz. For example, if the
* lowpass filter were a sinc function, Nc would be the index of the
* impulse-response lookup-table corresponding to the first zero-
* crossing of the sinc function. (The inverse first zero-crossing
* time of a sinc function equals its nominal cutoff frequency in Hz.)
* Nc must be a power of 2 due to the details of the current
* implementation. The default value of 128 is sufficiently high that
* using linear interpolation to fill in between the table entries
* gives approximately 16-bit precision, and quadratic interpolation
* gives about 23-bit (float) precision in filter coefficients.
*
* Lc - is log base 2 of Nc.
*
* La - is the number of bits devoted to linear interpolation of the
* filter coefficients.
*
* Lp - is La + Lc, the number of bits to the right of the binary point
* in the integer "time" variable. To the left of the point, it indexes
* the input array (X), and to the right, it is interpreted as a number
* between 0 and 1 sample of the input X. The default value of 23 is
* about right. There is a constraint that the filter window must be
* "addressable" in a int32_t, more precisely, if Nmult is the number
* of sinc zero-crossings in the right wing of the filter window, then
* (Nwing<<Lp) must be expressible in 31 bits.
*
*/
#define ISCALE 0x10000
/* 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;
double *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 */
unsigned long Xsize,Ysize; /* size (doubles) of X[],Y[] */
double *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(double 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
*/
static int getopts(sox_effect_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;
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)) {
return sox_usage(effp);
} else if ((r->rolloff <= 0.01) || (r->rolloff >= 1.0)) {
sox_fail("rolloff factor (%f) no good, should be 0.01<x<1.0", r->rolloff);
return(SOX_EOF);
}
if ((n >= 2) && !sscanf(argv[1], "%lf", &r->beta)) {
return sox_usage(effp);
} else if (r->beta <= 2.0) {
r->beta = 0;
sox_debug("opts: Nuttall window, cutoff %f", r->rolloff);
} else
sox_debug("opts: Kaiser window, cutoff %f, beta %f", r->rolloff, r->beta);
return (SOX_SUCCESS);
}
/*
* Prepare processing.
*/
static int start(sox_effect_t * effp)
{
resample_t r = (resample_t) effp->priv;
long Xoff, gcdrate;
int i;
if (effp->ininfo.rate == effp->outinfo.rate)
return SOX_EFF_NULL;
effp->outinfo.channels = effp->ininfo.channels;
r->Factor = effp->outinfo.rate / effp->ininfo.rate;
gcdrate = sox_gcd((long) effp->ininfo.rate, (long) effp->outinfo.rate);
r->a = effp->ininfo.rate / gcdrate;
r->b = effp->outinfo.rate / gcdrate;
if (r->a <= r->b && r->b <= NQMAX) {
r->quadr = -1; /* exact coeffs */
r->Nq = r->b; /* max(r->a,r->b) */
} else
r->Nq = Nc; /* for now */
/* Nwing: # of filter coeffs in right wing */
r->Nwing = r->Nq * (r->Nmult / 2 + 1) + 1;
r->Imp = (double *) xmalloc(sizeof(double) * (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) {
sox_fail("Unable to make filter");
return (SOX_EOF);
}
sox_debug("Nmult: %ld, Nwing: %ld, Nq: %ld", r->Nmult, r->Nwing, r->Nq);
if (r->quadr < 0) { /* exact coeff's method */
r->Xh = r->Nwing / r->b;
sox_debug("rate ratio %ld:%ld, coeff interpolation not needed", r->a, r->b);
} else {
r->dhb = Np; /* Fixed-point Filter sampling-time-increment */
if (r->Factor < 1.0)
r->dhb = 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 */
sox_fail("Factor is too small or large for BUFFSIZE");
return (SOX_EOF);
}
r->Xsize = 2 * Xoff + i / (1.0 + r->Factor);
r->Ysize = BUFFSIZE - r->Xsize;
sox_debug("Xsize %d, Ysize %d, Xoff %d", r->Xsize, r->Ysize, r->Xoff);
r->X = (double *) xmalloc(sizeof(double) * (BUFFSIZE));
r->Y = r->X + r->Xsize;
/* Need Xoff zeros at beginning of sample */
for (i = 0; i < Xoff; i++)
r->X[i] = 0;
return (SOX_SUCCESS);
}
/*
* Processed signed long samples from ibuf to obuf.
* Return number of samples processed.
*/
static int flow(sox_effect_t * effp, const sox_ssample_t *ibuf, sox_ssample_t *obuf,
sox_size_t *isamp, sox_size_t *osamp)
{
resample_t r = (resample_t) effp->priv;
long i, last, Nout, Nx, Nproc;
sox_debug_more("Xp %d, Xread %d, isamp %d, ",r->Xp, r->Xread,*isamp);
/* constrain amount we actually process */
Nproc = r->Xsize - r->Xp;
i = (r->Ysize < *osamp)? r->Ysize : *osamp;
if (Nproc * r->Factor >= i)
Nproc = i / r->Factor;
Nx = Nproc - r->Xread; /* space for right-wing future-data */
if (Nx <= 0)
{
sox_fail("Can not handle this sample rate change. Nx not positive: %d", Nx);
return (SOX_EOF);
}
if ((unsigned long)Nx > *isamp)
Nx = *isamp;
sox_debug_more("Nx %d",Nx);
if (ibuf == NULL) {
for(i = r->Xread; i < Nx + r->Xread ; i++)
r->X[i] = 0;
} else {
for(i = r->Xread; i < Nx + r->Xread ; i++)
r->X[i] = (double)(*ibuf++)/ISCALE;
}
last = i;
Nproc = last - r->Xoff - r->Xp;
if (Nproc <= 0) {
/* fill in starting here next time */
r->Xread = last;
/* leave *isamp alone, we consumed it */
*osamp = 0;
return (SOX_SUCCESS);
}
if (r->quadr < 0) { /* exact coeff's method */
long creep;
Nout = SrcEX(r, Nproc);
sox_debug_more("Nproc %d --> %d",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 */
sox_debug_more("Nproc %ld, creep %ld",Nproc,creep);
}
} else { /* approx coeff's method */
long creep;
Nout = SrcUD(r, Nproc);
sox_debug_more("Nproc %d --> %d",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 = r->Time - r->Xoff;
if (creep)
{
r->Time -= creep; /* Remove time accumulation */
r->Xp += creep; /* and add it to read pointer */
sox_debug_more("Nproc %ld, creep %ld",Nproc,creep);
}
}
{
long i,k;
/* Copy back portion of input signal that must be re-used */
k = r->Xp - r->Xoff;
sox_debug_more("k %d, last %d",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;
for(i=0; i < Nout; i++) {
double ftemp = r->Y[i] * ISCALE;
SOX_SAMPLE_CLIP_COUNT(ftemp, effp->clips);
*obuf++ = ftemp;
}
*isamp = Nx;
*osamp = Nout;
}
return (SOX_SUCCESS);
}
/*
* Process tail of input samples.
*/
static int drain(sox_effect_t * effp, sox_ssample_t *obuf, sox_size_t *osamp)
{
resample_t r = (resample_t) effp->priv;
long isamp_res, osamp_res;
sox_ssample_t *Obuf;
int rc;
sox_debug("Xoff %d <--- DRAIN",r->Xoff);
/* stuff end with Xoff zeros */
isamp_res = r->Xoff;
osamp_res = *osamp;
Obuf = obuf;
while (isamp_res>0 && osamp_res>0) {
sox_ssample_t Isamp, Osamp;
Isamp = isamp_res;
Osamp = osamp_res;
rc = flow(effp, NULL, Obuf, (sox_size_t *)&Isamp, (sox_size_t *)&Osamp);
if (rc)
return rc;
sox_debug("DRAIN isamp,osamp (%d,%d) -> (%d,%d)",
isamp_res,osamp_res,Isamp,Osamp);
Obuf += Osamp;
osamp_res -= Osamp;
isamp_res -= Isamp;
}
*osamp -= osamp_res;
sox_debug("DRAIN osamp %d", *osamp);
if (isamp_res)
sox_warn("drain overran obuf by %d", isamp_res);
/* FIXME: This is very picky. IF obuf is not big enough to
* drain remaining samples, they will be lost.
*/
return (SOX_EOF);
}
/*
* Do anything required when you stop reading samples.
* Don't close input file!
*/
static int stop(sox_effect_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 (SOX_SUCCESS);
}
/* over 90% of CPU time spent in this iprodUD() function */
/* quadratic interpolation */
static double qprodUD(const double Imp[], const double *Xp, long Inc, double T0,
long dhb, long ct)
{
const double f = 1.0/(1<<La);
double v;
long Ho;
Ho = T0 * dhb;
Ho += (ct-1)*dhb; /* so double sum starts with smallest coef's */
Xp += (ct-1)*Inc;
v = 0;
do {
double coef;
long Hoh;
Hoh = Ho>>La;
coef = Imp[Hoh];
{
double 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 double Imp[], const double *Xp, long Inc,
double T0, long dhb, long ct)
{
const double f = 1.0/(1<<La);
double v;
long Ho;
Ho = T0 * dhb;
Ho += (ct-1)*dhb; /* so double sum starts with smallest coef's */
Xp += (ct-1)*Inc;
v = 0;
do {
double 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)
{
double *Ystart, *Y;
double Factor;
double dt; /* Step through input signal */
double time;
double (*prodUD)(const double[], const double *, long, double, long, long);
int n;
prodUD = (r->quadr)? qprodUD:iprodUD; /* quadratic or linear interp */
Factor = r->Factor;
time = r->Time;
dt = 1.0/Factor; /* Output sampling period */
sox_debug_more("Factor %f, dt %f, ",Factor,dt);
sox_debug_more("Time %f, ",r->Time);
/* (Xh * dhb)>>La is max index into Imp[] */
sox_debug_more("ct=%.2f %d",(double)r->Nwing*Na/r->dhb, r->Xh);
sox_debug_more("ct=%ld, T=%.6f, dhb=%6f, dt=%.6f",
r->Xh, time-floor(time),(double)r->dhb/Na,dt);
Ystart = Y = r->Y;
n = (int)ceil((double)Nx/dt);
while(n--)
{
double *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;
sox_debug_more("Time %f",r->Time);
return (Y - Ystart); /* Return the number of output samples */
}
/* exact coeff's */
static double prodEX(const double Imp[], const double *Xp,
long Inc, long T0, long dhb, long ct)
{
double v;
const double *Cp;
Cp = Imp + (ct-1)*dhb + T0; /* so double 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)
{
double *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;
n = (Nx*b + (a-1))/a;
while(n--)
{
double *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(double 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 = floor((double)Nwing/(Num/Froll))*(Num/Froll) +0.5;
if (Mwing==0)
return(-4);
ImpR = (double *) xmalloc(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 */
sox_debug("DCgain err=%.12f",DCgain-1.0);
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);
}
}
}
const sox_effect_handler_t *sox_resample_effect_fn(void)
{
static sox_effect_handler_t handler = {
"resample", "[ -qs | -q | -ql ] [ rolloff [ beta ] ]",
SOX_EFF_RATE, getopts, start, flow, drain, stop, NULL
};
return &handler;
}