著者：斉藤 博文
プログラミング言語「AWK」は、データストリーム（データの流れ）を逐次処理するのに適しています。本連載では、電子回路の分野でその特徴を生かし、シェルスクリプトを組み合わせてデジタル信号を処理します。第3回は低周波成分を減らす「ハイパスフィルタ」について解説します。
シェルスクリプトマガジン Vol.81は以下のリンク先でご購入できます。
図7 ハイパスフィルタの移動平均プログラム（hpf.awk）
#! /usr/bin/gawk -f
BEGIN {
# define number of order
num_ord = num_ord ? num_ord : 255;
# define length of ring buffers
len_data_raw = num_ord + 1;
len_data_hpf = 2;
# initialize ring buffers
for (i = 0; i < len_data_raw; i++) {
arr_data_raw[i] = 0.0;
}
for (i = 0; i < len_data_hpf; i++) {
arr_data_hpf[i] = 0.0;
}
# initialize index of ring buffers
idx_data_raw = 0;
idx_data_hpf = 0;
# initialize number of data
num_data_raw = 0;
}
{
# add number of data
num_data_raw++;
# update index of ring buffers (write pointers)
idx_data_raw = num_data_raw % len_data_raw;
idx_data_hpf = num_data_raw % len_data_hpf;
# clear number of data
if (idx_data_raw == 0 && idx_data_hpf == 0) {
num_data_raw = 0;
}
# store input raw data
val_data_raw = $0;
arr_data_raw[idx_data_raw] = val_data_raw;
# apply high pass filter
arr_data_hpf[idx_data_hpf] = hpf( \
arr_data_raw, arr_data_hpf,
idx_data_raw, idx_data_hpf,
num_ord,
len_data_raw, len_data_hpf);
# print results
print arr_data_hpf[idx_data_hpf];
}
# get value of ring buffer
function get_buffer(arr, idx, len) {
if (idx < 0) {
return arr[idx + len];
}
return arr[idx];
}
# high pass filter
function hpf(arr_x, arr_y, idx_x, idx_y, ord, len_x, len_y, _ret, _gain) {
_ret = 0.0;
_gain = 1.0 / ord;
_ret += get_buffer(arr_y, idx_y - 1, len_y);
_ret -= _gain * get_buffer(arr_x, idx_x, len_x);
_ret += get_buffer(arr_x, idx_x - int((ord - 1) / 2), len_x);
_ret -= get_buffer(arr_x, idx_x - int((ord + 1) / 2), len_x);
_ret += _gain * get_buffer(arr_x, idx_x - ord, len_x);
return _ret;
}図12 群遅延を補正したプログラム（hpf_gd.awk）
#! /usr/bin/gawk -f
BEGIN {
# define number of order
num_ord = num_ord ? num_ord : 255;
# define group delay
val_gd = int((num_ord - 1) / 2);
# define length of ring buffers
len_data_raw = num_ord + 1;
len_data_hpf = val_gd + 1;
# initialize ring buffers
for (i = 0; i < len_data_raw; i++) {
arr_data_raw[i] = 0.0;
}
for (i = 0; i < len_data_hpf; i++) {
arr_data_hpf[i] = 0.0;
}
# initialize index of ring buffers
idx_data_raw = 0;
idx_data_hpf = 0;
# initialize number of data
num_data_raw = 0;
}
{
# add number of data
num_data_raw++;
# update index of ring buffers (write pointers)
idx_data_raw = num_data_raw % len_data_raw;
idx_data_hpf = num_data_raw % len_data_hpf;
# clear number of data
if (idx_data_raw == 0 && idx_data_hpf == 0) {
num_data_raw = 0;
}
# store input raw data
val_data_raw = $0;
arr_data_raw[idx_data_raw] = val_data_raw;
# apply high pass filter
arr_data_hpf[idx_data_hpf] = hpf( \
arr_data_raw, arr_data_hpf,
idx_data_raw, idx_data_hpf,
num_ord,
len_data_raw, len_data_hpf);
# print results
print get_buffer(arr_data_raw, idx_data_raw - val_gd, len_data_raw), arr_data_hpf[idx_data_hpf];
}
# get value of ring buffer
function get_buffer(arr, idx, len) {
if (idx < 0) {
return arr[idx + len];
}
return arr[idx];
}
# high pass filter
function hpf(arr_x, arr_y, idx_x, idx_y, ord, len_x, len_y, _ret, _gain) {
_ret = 0.0;
_gain = 1.0 / ord;
_ret += get_buffer(arr_y, idx_y - 1, len_y);
_ret -= _gain * get_buffer(arr_x, idx_x, len_x);
_ret += get_buffer(arr_x, idx_x - int((ord - 1) / 2), len_x);
_ret -= get_buffer(arr_x, idx_x - int((ord + 1) / 2), len_x);
_ret += _gain * get_buffer(arr_x, idx_x - ord, len_x);
return _ret;
}
