Band limited waveform sample generation

band_lim_wav.py

import math
import csv
import StringIO
import random


def sinc(x):
    theta = 2.0 * x * math.pi * 4.0
    try:
        return min(1.0, math.sin(theta) / theta)
    except:
        return 1.0


def gen_sync():
    y = [0] * 256
    for i, x in enumerate(range(-128, 128)):
        atten = math.cos((float(abs(x)) / 128.0) * math.pi * 0.5)
        y[i] = sinc(float(x) / 128) * atten
    return y


def write_sync():
    y = gen_sync()
    # write output
    with open('out.csv', 'wb') as f:
        for d in y:
            f.write('{:f}'.format(d))
            f.write(',')


def fourier_tri(x, nyquist):
    limit = nyquist * 2.0 * math.pi
    v = 0.0
    for i in range(0, 50):
        n = 2.0 * i + 1.0
        theta = 2.0 * math.pi * n
        if theta > limit:
            break
        s = math.pow(-1, i)
        l = math.pow(n, -2)
        v += s * l * math.sin(theta * x)
    return v


def fourier_saw(x, nyquist):
    limit = nyquist * 2.0 * math.pi
    v = 0.0
    for k in range(1, 50, 1):
        theta = 2.0 * math.pi * float(k)
        if theta > limit:
            break
        n = 1 if (k % 1 == 0) else -1
        v += n * math.sin(theta * x) / float(k)
    return (2.0 / math.pi) * v


def fourier_sqr(x, nyquist):
    limit = nyquist * 2.0 * math.pi
    v = 0.0
    for k in range(1, 50, 2):
        theta = 2.0 * math.pi * float(k)
        if theta > limit:
            break
        v += math.sin(theta * x) / float(k)
    return (4.0 / math.pi) * v


def gen_fourier(samples, func):
    out = [0.0] * samples
    offset = 0.5 / float(samples)
    for i in range(0, samples):
        x = (float(i) / float(samples)) + offset
        out[i] = func(x, samples // 2)
    return out


def fmt_sample(x):
    return '{}{:04x}'.format(
        '-0x' if x < 0 else ' 0x',
        abs(int(x * 0x3fff + random.uniform(-1.2, 1.2))))


def write_array(prefix, width, func, fmt, stream):
    y = gen_fourier(width, func)
    stream.write('static const int16_t {}{}[] = {{'.format(prefix, width))
    for i, v in enumerate(y):
        if i > 0:
            stream.write(', ')
        if i % 8 == 0:
            stream.write('\n  ')
        stream.write('{}'.format(fmt(v)))
    stream.write('};')


def dump_c_arrays():
    stream = StringIO.StringIO()
    # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
    width = 1024
    while width > 1:
        write_array('bl_sqr_', width, fourier_sqr, fmt_sample, stream)
        stream.write('\n\n')
        width /= 2
    # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
    width = 1024
    while width > 1:
        write_array('bl_saw_', width, fourier_saw, fmt_sample, stream)
        stream.write('\n\n')
        width /= 2
    # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
    width = 1024
    while width > 1:
        write_array('bl_tri_', width, fourier_tri, fmt_sample, stream)
        stream.write('\n\n')
        width /= 2
    # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
    with file('tables.c', 'w') as fd:
        fd.write(stream.getvalue())


def dump_csv_files():
    width = 1024
    while width > 1:
        y = gen_fourier(width, fourier_sqr)
        # write output
        name = 'sqr_{}.csv'.format(width)
        with open(name, 'wb') as f:
            for d in y:
                f.write('{:f}'.format(d))
                f.write(',')
        # next level of mip
        width /= 2


if __name__ == '__main__':
    dump_c_arrays()