#!/usr/bin/python2.5 # # Copyright 2014 Olivier Gillet. # # Author: Olivier Gillet (ol.gillet@gmail.com) # # 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. # # See http://creativecommons.org/licenses/MIT/ for more information. # # ----------------------------------------------------------------------------- # # Waveform definitions. import numpy waveforms = [] """---------------------------------------------------------------------------- Sine wave ----------------------------------------------------------------------------""" WAVETABLE_SIZE=1024 x = numpy.arange(0, WAVETABLE_SIZE + 1) / float(WAVETABLE_SIZE) x[-1] = x[0] sine = numpy.sin(2 * numpy.pi * x) waveforms.append(('sine1024', (32767 * sine).astype(int))) WAVETABLE_SIZE=128 x = numpy.arange(0, WAVETABLE_SIZE + 1) / float(WAVETABLE_SIZE) x[-1] = x[0] sine = numpy.sin(2 * numpy.pi * x) waveforms.append(('sine128', (32767 * sine).astype(int))) WAVETABLE_SIZE=64 x = numpy.arange(0, WAVETABLE_SIZE + 1) / float(WAVETABLE_SIZE) x[-1] = x[0] sine = numpy.sin(2 * numpy.pi * x) waveforms.append(('sine64', (32767 * sine).astype(int))) WAVETABLE_SIZE=16 x = numpy.arange(0, WAVETABLE_SIZE + 1) / float(WAVETABLE_SIZE) x[-1] = x[0] sine = numpy.sin(2 * numpy.pi * x) waveforms.append(('sine16', (32767 * sine).astype(int))) """---------------------------------------------------------------------------- Band-limited waveforms ----------------------------------------------------------------------------""" SAMPLE_RATE = 48000.0 WAVETABLE_SIZE = 1024 def dither(x, order=0, type=numpy.int16): for i in xrange(order): x = numpy.hstack((numpy.zeros(1,), numpy.cumsum(x))) x = numpy.round(x) for i in xrange(order): x = numpy.diff(x) if any(x < numpy.iinfo(type).min) or any(x > numpy.iinfo(type).max): print 'Clipping occurred!' x[x < numpy.iinfo(type).min] = numpy.iinfo(type).min x[x > numpy.iinfo(type).max] = numpy.iinfo(type).max return x.astype(type) def scale(array, min=-32766, max=32766, center=True, dither_level=2): if center: array -= array.mean() mx = numpy.abs(array).max() array = (array + mx) / (2 * mx) array = array * (max - min) + min return dither(array, order=dither_level) # Band limited waveforms. num_zones = 20 bl_parabola_tables = [] wrap = numpy.arange(WAVETABLE_SIZE + 1) + WAVETABLE_SIZE / 2 wrap = numpy.fmod(wrap, WAVETABLE_SIZE) quadrature = numpy.arange(WAVETABLE_SIZE + 1) + WAVETABLE_SIZE / 4 quadrature = numpy.fmod(quadrature, WAVETABLE_SIZE) fill = numpy.arange(WAVETABLE_SIZE + 1) fill = numpy.fmod(fill, WAVETABLE_SIZE) ref_f0_energy = None for zone in range(num_zones): f0 = 440.0 * 2.0 ** ((8 + 8 * zone - 69) / 12.0) f0 = min(f0, SAMPLE_RATE / 2.0) period = SAMPLE_RATE / f0 m = 2 * numpy.floor(period / 2) + 1.0 i = numpy.arange(-WAVETABLE_SIZE / 2, WAVETABLE_SIZE / 2) / \ float(WAVETABLE_SIZE) pulse = numpy.sin(numpy.pi * i * m) / (m * numpy.sin(numpy.pi * i) + 1e-9) pulse[WAVETABLE_SIZE / 2] = 1.0 pulse = pulse[fill] square = numpy.cumsum(pulse - pulse[wrap]) triangle = -numpy.cumsum(square[::-1] - square.mean()) / WAVETABLE_SIZE saw = -numpy.cumsum(pulse[wrap] - pulse.mean()) parabola = numpy.cumsum(saw - saw.mean()) scaled_parabola = scale(parabola[quadrature]) f0_energy = numpy.abs(numpy.fft.rfft(scaled_parabola)[1]) if ref_f0_energy is None: ref_f0_energy = f0_energy scaled_parabola = scaled_parabola / f0_energy * ref_f0_energy scaled_parabola *= min(1.0, 32767 / scaled_parabola.max()) bl_parabola_tables.append( ('bandlimited_parabola_%d' % zone, scaled_parabola)) waveforms.extend(bl_parabola_tables) """---------------------------------------------------------------------------- Waveshaper for audio rate ----------------------------------------------------------------------------""" WAVESHAPER_SIZE = 1024 x = numpy.arange(0, WAVESHAPER_SIZE + 1) / float(WAVESHAPER_SIZE) linear = x sin = (1.0 - numpy.cos(numpy.pi * x)) / 2.0 tan = numpy.arctan(8 * numpy.cos(numpy.pi * x)) scale = tan.max() tan = (1.0 - tan / scale) / 2.0 inverse_sin = numpy.arccos(1 - 2 * x) / numpy.pi inverse_tan = numpy.arccos(numpy.tan(scale * (1.0 - 2.0 * x)) / 8.0) / numpy.pi def audio_rate_flip(x): x = numpy.array(list(-x[WAVESHAPER_SIZE:0:-1]) + list(x)) return numpy.round((x * 32767.0)).astype(int) audio_rate_tables = [] audio_rate_tables.append(('inverse_tan_audio', audio_rate_flip(inverse_tan))) audio_rate_tables.append(('inverse_sin_audio', audio_rate_flip(inverse_sin))) audio_rate_tables.append(('linear_audio', audio_rate_flip(linear))) audio_rate_tables.append(('sin_audio', audio_rate_flip(sin))) audio_rate_tables.append(('tan_audio', audio_rate_flip(tan))) waveforms.extend(audio_rate_tables) """---------------------------------------------------------------------------- Waveshaper for control rate ----------------------------------------------------------------------------""" WAVESHAPER_SIZE = 512 x = numpy.arange(0, WAVESHAPER_SIZE + 1) / float(WAVESHAPER_SIZE) linear = x sin = (1.0 - numpy.cos(numpy.pi * x)) / 2.0 inverse_sin = numpy.arccos(1 - 2 * x) / numpy.pi inverse_sin = (((inverse_sin*2-1) ** 3)+1)*0.5 # for more contrast expo = 1.0 - numpy.exp(-3 * x) expo_max = expo.max() expo = 1.0 - (1.0 - expo) ** 2 # for more contrast expo /= expo.max() expo_flipped = 1.0 - numpy.exp(-3 * (1 - x)) expo_flipped = 1.0 - (1.0 - expo_flipped) ** 2 # for more contrast expo_flipped /= expo_flipped.max() log = numpy.log(1.0 - x * expo_max) / -3.0 log -= log.min() log /= log.max() log = log ** 2 # for more contrast log_flipped = numpy.log(1.0 - (1 - x) * expo_max) / -3.0 log_flipped -= log_flipped.min() log_flipped /= log_flipped.max() log_flipped = log_flipped ** 2 # for more contrast def control_rate_flip(x, y): x = numpy.array(list(x) + list(y[1:])) return numpy.round((x * 32767.0)).astype(int) control_rate_tables = [] control_rate_tables.append( ('reversed_control', control_rate_flip(log, 1.0 - log))) control_rate_tables.append( ('spiky_exp_control', control_rate_flip(log, log_flipped))) control_rate_tables.append( ('spiky_control', control_rate_flip(inverse_sin, 1.0 - inverse_sin))) control_rate_tables.append( ('linear_control', control_rate_flip(linear, 1.0 - linear))) control_rate_tables.append( ('bump_control', control_rate_flip(sin, 1.0 - sin))) control_rate_tables.append( ('bump_exp_control', control_rate_flip(expo, expo_flipped))) control_rate_tables.append( ('normal_control', control_rate_flip(expo, 1.0 - expo))) waveforms.extend(control_rate_tables) """---------------------------------------------------------------------------- Post waveshaper ----------------------------------------------------------------------------""" WAVESHAPER_SIZE = 1024 x = numpy.arange(0, WAVESHAPER_SIZE + 1) / (WAVESHAPER_SIZE / 2.0) - 1.0 x[-1] = x[-2] sine = numpy.sin(8 * numpy.pi * x) window = numpy.exp(-x * x * 4) ** 2 bipolar_fold = sine * window + numpy.arctan(3 * x) * (1 - window) bipolar_fold /= numpy.abs(bipolar_fold).max() waveforms.append(('bipolar_fold', numpy.round(32767 * bipolar_fold))) x = numpy.arange(0, WAVESHAPER_SIZE + 1) / float(WAVESHAPER_SIZE) x[-1] = x[-2] sine = numpy.sin(8 * numpy.pi * x) window = numpy.exp(-x * x * 4) ** 2 unipolar_fold = (0.5 * sine + 2 * x) * window + numpy.arctan(4 * x) * (1 - window) unipolar_fold /= numpy.abs(unipolar_fold).max() waveforms.append(('unipolar_fold', numpy.round(32767 * unipolar_fold)))