but i need to get this far a lot! and get farther!
my longer term project was the flat_tree thing for random-write
append-only media.
now that i've successfully made some forensic math, maybe i can
preserve all the trash or whatever using that.
here's fourier.py for finding later.
next step would be adding streaming, so that it preserves phase
changes when re-applied to a following chunk, accumulating data
accurately. that just means multiplying by an array that has
components with appropriate complex phases.
# AGPL-3 Karl Semich 2022
import numpy as np
def create_freq2time(freq_rate, time_rate, freq_count, time_count):
freqs = np.fft.fftfreq(freq_count)
offsets = np.arange(freq_count) * freq_rate / time_rate
mat = np.exp(2j * np.pi * np.outer(freqs, offsets))
return mat / freq_count # scaled to match numpy convention
def create_time2freq(time_rate, freq_rate, time_count, freq_count):
if time_count != freq_count:
raise NotImplementedError("differing input and output samplecounts")
forward_mat = create_freq2time(freq_rate, time_rate, freq_count, time_count)
reverse_mat = np.linalg.inv(forward_mat)
return reverse_mat
def test():
np.random.seed(0)
randvec = np.random.random(16)
ift16 = create_freq2time(1, 1, 16, 16)
ft16 = create_time2freq(1, 1, 16, 16)
randvec2time = randvec @ ift16
randvec2freq = randvec @ ft16
randvec2ifft = np.fft.ifft(randvec)
randvec2fft = np.fft.fft(randvec)
assert np.allclose(randvec2ifft, randvec2time)
assert np.allclose(randvec2fft, randvec2freq)
# sample data at a differing rate
time_rate = np.random.random() * 2
freq_rate = 1.0
freqs = np.fft.fftfreq(len(randvec))
rescaling_ift = create_freq2time(freq_rate, time_rate, len(randvec), len(randvec))
rescaling_ft = create_time2freq(time_rate, freq_rate, len(randvec), len(randvec))
rescaled_time_data = np.array([
np.mean([
randvec[freqidx] * np.exp(2j * np.pi * freqs[freqidx] * sampleidx / time_rate)
for freqidx in range(len(randvec))
])
for sampleidx in range(len(randvec))
])
assert np.allclose(rescaled_time_data, randvec @ rescaling_ift)
unscaled_freq_data = rescaled_time_data @ rescaling_ft
unscaled_time_data = unscaled_freq_data @ ift16
assert np.allclose(unscaled_freq_data, randvec)
assert np.allclose(unscaled_time_data, randvec2time)
if __name__ == '__main__':
test()
