def get_phase(cfg):
read = WaveReader(WAVE_DIR, cfg)
instr = read.read()
spectrum = rfft_norm(instr.waves[0])
phase = np.angle(spectrum[1])
return phase
def test_reader_multi_waves():
cfg_str = '''\
files:
- path: sine440.69.wav
- path: sine440.69.wav
speed: 2
volume: 1.1
- path: sine256.59.624.wav
speed: 3
volume: 0
pitch_estimate: 69
nwave: 1
nsamp: 16
'''
harmonics = [1, 2] # plus 3 at volume=0
cfg = n163_cfg(**yaml.load(cfg_str))
read = WaveReader(WAVE_DIR, cfg)
instr = read.read()
# Calculate spectrum of resulting signal
spectrum: np.ndarray = np.abs(rfft_norm(instr.waves[0]))
spectrum[0] = 0
threshold = np.amax(spectrum) / 2
assert threshold > 0.1
# Ensure pitches present
assert (spectrum[harmonics] > threshold).all()
# Ensure no other pitches present
spectrum[harmonics] = 0
spectrum[0] = 0
assert (spectrum < threshold).all()
def _get_periodic_fft_freq(self, data) -> Tuple[SpectrumType, float]:
""" Returns periodic FFT and frequency (Hz) of data. """
# Number of samples
nsamp = self.wcfg.nsamp
freq_mul = self.freq_mul
mode = self.cfg.mode
periodic_fft = []
fundamental_bin: float = self._get_fundamental_bin(data)
if mode == 'stft':
# Get STFT.
stft = self._stft(data)
# Convert STFT to periodic FFT.
for harmonic in range(rfft_length(nsamp, freq_mul)):
begin = fundamental_bin * (harmonic - 0.5)
end = fundamental_bin * (harmonic + 0.5)
bands = stft[math.ceil(begin):math.ceil(end)]
amplitude: complex = self.power_sum(bands)
periodic_fft.append(amplitude)
elif mode == 'cycle':
period = round(len(data) / fundamental_bin)
# Pick 1 period of data, from the middle of the region.
end = (len(data) + period) // 2
begin = end - period
periodic_fft = fourier.rfft_norm(data[begin:end])
else:
raise ValueError(f'mode=[stft, cycle] (you supplied {mode})')
# Multiply pitch of FFT.
freq_mul_fft = zero_pad(periodic_fft, freq_mul)
# Ensure we didn't omit any harmonics <= Nyquist.
if mode == 'stft':
fft_plus_harmonic_length = len(freq_mul_fft) + freq_mul
assert fft_plus_harmonic_length > rfft_length(nsamp), \
f'fft len={len(freq_mul_fft)} + {freq_mul} not > {rfft_length(nsamp)}'
# cyc/s = cyc/bin * bin/samp * samp/s
freq_hz = fundamental_bin / len(data) * self.smp_s
return freq_mul_fft, freq_hz
def filter_wave(wave: WaveType, transfer) -> WaveType:
harm = fourier.rfft_norm(wave)
harm[1:] *= transfer(np.arange(1, len(harm)))
return fourier.irfft_norm(harm)
def _stft(self, data: np.ndarray) -> np.ndarray:
""" Phasor phases will match center of data, or peak of window. """
data *= self.window
phased_data = np.roll(data, len(data) // 2)
return fourier.rfft_norm(phased_data)
def test_repeat():
cat = rfft_zoh(pulse * 3)
pad = zero_pad(rfft_zoh(pulse), 3)
assert_close(cat, pad)
assert not np.allclose(cat, rfft_norm(pulse * 3))
def test_irfft():
zoh1 = rfft_norm(pulse)
zoh3 = zero_pad(zoh1, 3)
ipulse3 = irfft_norm(zoh3)
assert_close(ipulse3, pulse3)
# noinspection PyUnresolvedReferences
import numpy as np
from wavetable.dsp.fourier import zero_pad, rfft_norm, irfft_norm, rfft_zoh, irfft_zoh, \
nyquist_real_idx, rfft_length
def assert_close(a, b):
assert len(a) == len(b)
assert np.allclose(a, b)
pulse = [1, 0, 0, 0]
pulse3 = pulse * 3
expected = [0.25] * 3
fft1 = rfft_norm(pulse)
assert_close(fft1, expected)
def test_nyquist_real():
assert nyquist_real_idx(4) == 2
assert nyquist_real_idx(5) == 3
def test_nyquist_inclusive():
assert rfft_length(4) == 3
assert rfft_length(5) == 3
# A 16-sample wave has harmonics [0..8] with length 9.
assert rfft_length(16, 1) == 9