firhalfband.jsfx-inc

desc:FIR Filter Half Band
/*
  FIR Half band filter

  The MIT License (MIT)

  Copyright (c) 2021 Justin Johnson

  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:

  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.

  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.

  ---
 
  Reference: http://www.labbookpages.co.uk/audio/firWindowing.html
 
  This filter is designed to do one job and do it well and as fast as JSFX can muster (almost).
 
   It's a half band low pass 65 tap FIR filter meant for use with oversampling x2.
 
   For 44.1Khz: At 88.2kHz it filters out frequencies after 22050hz which gets rid of aliasing introduced
   by zero filling when oversampling.
 
   The filter is steep and uses the following vars (44.1kHz):
 
   Fa = 0
   Fb = 22050
   length = 65
   Fs = 88200
   Att = 96db
 
   From here:
 
     http://arc.id.au/FilterDesign.html
 
   Example:
  
   // DAW sample rate 44.1kHz (left channel given, same for right channel)
   // Oversampling x 2
 
   @init
   firL.init_FIR_filter_44100();
 
   @sample
   y0 = left.do_process(spl0);   // Apply application filters and other processing etc
   y1 = left.do_process(0);      // Zero padding
 
   spl0 = firL.do_FIR_filter(y0) * 2;  // First fir application
   firL.do_FIR_filter(y1);             // Discard (crude decimation, only do this if you're
                                       // not generating harmonics, ie. clean EQ)

 */

@init

function init_FIR_filter_44100()
  instance(
    b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19,
    b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35, b36, b37, b38, b39,
    b40, b41, b42, b43, b44, b45, b46, b47, b48, b49, b50, b51, b52, b53, b54, b55, b56, b57, b58, b59,
    b60, b61, b62, b63, b64,
    w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19,
    w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32
  )
(
  // Set the FIR window taking into account symmetry around the centre tap (w32).
  w0  = -0.000000;
  w1  = -0.000016; 
  w2  = 0.000000;
  w3  = 0.000067; 
  w4  = -0.000000; 
  w5  = -0.000189; 
  w6  = -0.000000; 
  w7  = 0.000438;
  w8  = -0.000000; 
  w9  = -0.000891; 
  w10 = 0.000000; 
  w11 = 0.001653; 
  w12 = -0.000000; 
  w13 = -0.002862; 
  w14 = 0.000000; 
  w15 = 0.004690; 
  w16 = -0.000000; 
  w17 = -0.007364; 
  w18 = 0.000000; 
  w19 = 0.011189; 
  w20 = -0.000000; 
  w21 = -0.016631; 
  w22 = 0.000000; 
  w23 = 0.024500; 
  w24 = -0.000000; 
  w25 = -0.036479; 
  w26 = 0.000000; 
  w27 = 0.056928; 
  w28 = -0.000000; 
  w29 = -0.101933; 
  w30 = 0.000000; 
  w31 = 0.316897; 
  w32 = 0.500000; 
);

function init_FIR_filter_48000()
  instance(
    b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19,
    b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35, b36, b37, b38, b39,
    b40, b41, b42, b43, b44, b45, b46, b47, b48, b49, b50, b51, b52, b53, b54, b55, b56, b57, b58, b59,
    b60, b61, b62, b63, b64,
    w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19,
    w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32
  )
(
  // Set the FIR window taking into account symmetry around the centre tap (w32).

  w0  = -0.000005; 
  w1  = 0.000006;
  w2  = 0.000034; 
  w3  = -0.000015; 
  w4  = -0.000115; 
  w5  = 0.000020; 
  w6  = 0.000293; 
  w7  = 0.000007; 
  w8  = -0.000631; 
  w9  = -0.000125; 
  w10 = 0.001200; 
  w11 = 0.000433; 
  w12 = -0.002076; 
  w13 = -0.001087; 
  w14 = 0.003317; 
  w15 = 0.002305; 
  w16 = -0.004952; 
  w17 = -0.004386; 
  w18 = 0.006964; 
  w19 = 0.007728; 
  w20 = -0.009278; 
  w21 = -0.012890; 
  w22 = 0.011759; 
  w23 = 0.020763; 
  w24 = -0.014222; 
  w25 = -0.033078; 
  w26 = 0.016454; 
  w27 = 0.054199; 
  w28 = -0.018238; 
  w29 = -0.100165; 
  w30 = 0.019392; 
  w31 = 0.316285; 
  w32 = 0.480208; 
);

function do_FIR_filter_less_efficient(input)
  instance(
    b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19,
    b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35, b36, b37, b38, b39,
    b40, b41, b42, b43, b44, b45, b46, b47, b48, b49, b50, b51, b52, b53, b54, b55, b56, b57, b58, b59,
    b60, b61, b62, b63, b64,
    w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19,
    w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32
  )  
(
  // Scroll the window
  b64 = b63; b63 = b62; b62 = b61; b61 = b60;
  b60 = b59; b59 = b58; b58 = b57; b57 = b56; b56 = b55; b55 = b54; b54 = b53; b53 = b52; b52 = b51; b51 = b50;
  b50 = b49; b49 = b48; b48 = b47; b47 = b46; b46 = b45; b45 = b44; b44 = b43; b43 = b42; b42 = b41; b41 = b40;
  b40 = b39; b39 = b38; b38 = b37; b37 = b36; b36 = b35; b35 = b34; b34 = b33; b33 = b32; b32 = b31; b31 = b30;
  b30 = b29; b29 = b28; b28 = b27; b27 = b26; b26 = b25; b25 = b24; b24 = b23; b23 = b22; b22 = b21; b21 = b20;
  b20 = b19; b19 = b18; b18 = b17; b17 = b16; b16 = b15; b15 = b14; b14 = b13; b13 = b12; b12 = b11; b11 = b10;
  b10 = b9; b9 = b8; b8 = b7; b7 = b6; b6 = b5; b5 = b4; b4 = b3; b3 = b2; b2 = b1; b1 = b0;

  // Introduce the new sample into the window
  b0 = input;

  // Compute and return, taking advantage of symmetrical fir filter to reduce operations 
  w0 * (b0 + b64) + w1 * (b1 + b63) + w2 * (b2 + b62) + w3 * (b3 + b61) + w4 * (b4 + b60) + w5 * (b5 + b59) + w6 * (b6 + b58) +
  w7 * (b7 + b57) + w8 * (b8 + b56) + w9 * (b9 + b55) + w10 * (b10 + b54) + w11 * (b11 + b53) + w12 * (b12 + b52) + w13 * (b13 + b51) +
  w14 * (b14 + b50) + w15 * (b15 + b49) + w16 * (b16 + b48) + w17 * (b17 + b47) + w18 * (b18 + b46) + w19 * (b19 + b45) + w20 * (b20 + b44) +
  w21 * (b21 + b43) + w22 * (b22 + b42) + w23 * (b23 + b41) + w24 * (b24 + b40) + w25 * (b25 + b39) + w26 * (b26 + b38) + w27 * (b27 + b37) +
  w28 * (b28 + b36) + w29 * (b29 + b35) + w30 * (b30 + b34) + w31 * (b31 + b33) + w32 * (b32);
);

function do_FIR_filter(input0, input1) local(ret)
  instance(
    b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16, b17, b18, b19,
    b20, b21, b22, b23, b24, b25, b26, b27, b28, b29, b30, b31, b32, b33, b34, b35, b36, b37, b38, b39,
    b40, b41, b42, b43, b44, b45, b46, b47, b48, b49, b50, b51, b52, b53, b54, b55, b56, b57, b58, b59,
    b60, b61, b62, b63, b64,
    w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19,
    w20, w21, w22, w23, w24, w25, w26, w27, w28, w29, w30, w31, w32
  )  
(
  // Compute and return.
  // We're zero padding so only interest in the result of input0
  // Taking advantage of symmetrical fir filter to reduce operations.
  // We also arrange operations so that we don't need to scroll the window before calculating.
  ret = w0 * (input0 + b63) + w1 * (b0 + b62) + w2 * (b1 + b61) + w3 * (b2 + b60) + w4 * (b3 + b59) + w5 * (b4 + b58) + w6 * (b5 + b57) +
  w7 * (b6 + b56) + w8 * (b7 + b55) + w9 * (b8 + b54) + w10 * (b9 + b53) + w11 * (b10 + b52) + w12 * (b11 + b51) + w13 * (b12 + b50) +
  w14 * (b13 + b49) + w15 * (b14 + b48) + w16 * (b15 + b47) + w17 * (b16 + b46) + w18 * (b17 + b45) + w19 * (b18 + b44) + w20 * (b19 + b43) +
  w21 * (b20 + b42) + w22 * (b21 + b41) + w23 * (b22 + b40) + w24 * (b23 + b39) + w25 * (b24 + b38) + w26 * (b25 + b37) + w27 * (b26 + b36) +
  w28 * (b27 + b35) + w29 * (b28 + b34) + w30 * (b29 + b33) + w31 * (b30 + b32) + w32 * (b31);

  // Scroll the window by two
  b64 = b62; b63 = b61; b62 = b60; b61 = b59;
  b60 = b58; b59 = b57; b58 = b56; b57 = b55; b56 = b54; b55 = b53; b54 = b52; b53 = b51; b52 = b50; b51 = b49;
  b50 = b48; b49 = b47; b48 = b46; b47 = b45; b46 = b44; b45 = b43; b44 = b42; b43 = b41; b42 = b40; b41 = b39;
  b40 = b38; b39 = b37; b38 = b36; b37 = b35; b36 = b34; b35 = b33; b34 = b32; b33 = b31; b32 = b30; b31 = b29;
  b30 = b28; b29 = b27; b28 = b26; b27 = b25; b26 = b24; b25 = b23; b24 = b22; b23 = b21; b22 = b20; b21 = b19;
  b20 = b18; b19 = b17; b18 = b16; b17 = b15; b16 = b14; b15 = b13; b14 = b12; b13 = b11; b12 = b10; b11 = b9;
  b10 = b8;  b9 =  b7;  b8 =  b6;  b7 =  b5;  b6  = b4;  b5  = b3;  b4  = b2;  b3  = b1;  b2  = b0;

  b1 = input0;
  b0 = input1;

  // Filtering out the mirror beyond Nyquist reduces energy by half so multiply back out
  ret * 2.0;
);

function get_FIR_pdc() ( 
  // PDC is usually number of taps / 2 (that's 32)
  // We'll be running x2 so the delay is halved again.
  16;
);

// Included the un-rolled source code here for completeness and in case any other work
// on coefficients etc is required.
/*
function init_FIR_filter(bufmem, ntaps, coeffs)
  instance(hist_buf, buf_ptr, buf_ptr2, len, w)
(
  len = ntaps;
  hist_buf = bufmem;
  buf_ptr = hist_buf + (len-1);
  buf_ptr2 = buf_ptr + len;
  w = coeffs;

  w[0] = w[64] = -0.000000;
  w[1] = w[63] = -0.000016; 
  w[2] = w[62] = 0.000000;
  w[3] = w[61] = 0.000067; 
  w[4] = w[60] = -0.000000; 
  w[5] = w[59] = -0.000189; 
  w[6] = w[58] = -0.000000; 
  w[7] = w[57] = 0.000438;
  w[8] = w[56] = -0.000000; 
  w[9] = w[55] = -0.000891; 
  w[10] = w[54] = 0.000000; 
  w[11] = w[53] = 0.001653; 
  w[12] = w[52] = -0.000000; 
  w[13] = w[51] = -0.002862; 
  w[14] = w[50] = 0.000000; 
  w[15] = w[49] = 0.004690; 
  w[16] = w[48] = -0.000000; 
  w[17] = w[47] = -0.007364; 
  w[18] = w[46] = 0.000000; 
  w[19] = w[45] = 0.011189; 
  w[20] = w[44] = -0.000000; 
  w[21] = w[43] = -0.016631; 
  w[22] = w[42] = 0.000000; 
  w[23] = w[41] = 0.024500; 
  w[24] = w[40] = -0.000000; 
  w[25] = w[39] = -0.036479; 
  w[26] = w[38] = 0.000000; 
  w[27] = w[37] = 0.056928; 
  w[28] = w[36] = -0.000000; 
  w[29] = w[35] = -0.101933; 
  w[30] = w[34] = 0.000000; 
  w[31] = w[33] = 0.316897; 
  w[32] = 0.500000; 
);

function do_FIR_filter(s0)
  local(sum, n)
  instance(hist_buf, buf_ptr, buf_ptr2, len, w)  
(
  buf_ptr[] = buf_ptr2[] = s0;

  sum = n = 0;
  loop(len,
    sum += w[n] * buf_ptr[n];
    n += 1;
  );

  buf_ptr -= 1; buf_ptr2 -= 1;
  buf_ptr < hist_buf ? (
    buf_ptr = hist_buf + (len-1);
    buf_ptr2 = buf_ptr + len;
  );

  sum;
);

// Read coefficients from file using:
handle = file_open("coff.txt");

len = file_mem(handle, wm, 65);

file_close(handle);

m = len - 1;

// Was the following normalisation really needed??
n = 1;
normalize = w[0];
loop(len,
  normalize += w[n];
  n += 1;
);

n = 0;
normalize = 1/normalize;
loop(len,
  w[n] *= normalize;
  n += 1;
);
*/