src/band.h

   1 /* libSoX Bandpass effect file.     July 5, 1991
   2  * Copyright 1991 Lance Norskog And Sundry Contributors
   3  *
   4  * This source code is freely redistributable and may be used for
   5  * any purpose.  This copyright notice must be maintained.
   6  * Lance Norskog And Sundry Contributors are not responsible for
   7  * the consequences of using this software.
   8  *
   9  * Algorithm:  2nd order recursive filter.
  10  * Formula stolen from MUSIC56K, a toolkit of 56000 assembler stuff.
  11  * Quote:
  12  *   This is a 2nd order recursive band pass filter of the form.
  13  *   y(n)= a * x(n) - b * y(n-1) - c * y(n-2)
  14  *   where :
  15  *        x(n) = "IN"
  16  *        "OUT" = y(n)
  17  *        c = EXP(-2*pi*cBW/S_RATE)
  18  *        b = -4*c/(1+c)*COS(2*pi*cCF/S_RATE)
  19  *   if cSCL=2 (i.e. noise input)
  20  *        a = SQT(((1+c)*(1+c)-b*b)*(1-c)/(1+c))
  21  *   else
  22  *        a = SQT(1-b*b/(4*c))*(1-c)
  23  *   endif
  24  *   note :     cCF is the center frequency in Hertz
  25  *        cBW is the band width in Hertz
  26  *        cSCL is a scale factor, use 1 for pitched sounds
  27  *   use 2 for noise.
  28  *
  29  *
  30  * July 1, 1999 - Jan Paul Schmidt <jps@fundament.org>
  31  *
  32  *   This looks like the resonator band pass in SPKit. It's a
  33  *   second order all-pole (IIR) band-pass filter described
  34  *   at the pages 186 - 189 in
  35  *     Dodge, Charles & Jerse, Thomas A. 1985:
  36  *       Computer Music -- Synthesis, Composition and Performance.
  37  *       New York: Schirmer Books.
  38  *   Reference from the SPKit manual.
  39  */
  40
  41   p->a2 = exp(-2 * M_PI * bw_Hz / effp->in_signal.rate);
  42   p->a1 = -4 * p->a2 / (1 + p->a2) * cos(2 * M_PI * p->fc / effp->in_signal.rate);
  43   p->b0 = sqrt(1 - p->a1 * p->a1 / (4 * p->a2)) * (1 - p->a2);
  44   if (p->filter_type == filter_BPF_SPK_N) {
  45     mult = sqrt(((1+p->a2) * (1+p->a2) - p->a1*p->a1) * (1-p->a2) / (1+p->a2)) / p->b0;
  46     p->b0 *= mult;
  47   }