the comparison is failing, [although the sample_idcs look right now,]
so given fourier.py passes its internal tests, the difference must lie
in how waveform is being sampled compared to the assumptions that
fourier.py is making
0843
i can go into both functions and again examine the first few data items
7 def sample_sinusoids_funny(data, fractional_indices, max_period):
8 -> return np.array([
9 ((np.exp(2j * sample_idx * np.pi *
np.fft.fftfreq(len(data)))) * np.fft.fft(data)).sum() / len(data) for
sample_idx in fractional_indices
10 ])
(Pdb) p data
array([0.5488135 , 0.71518937, 0.60276338, 0.54488318, 0.4236548 ,
0.64589411, 0.43758721, 0.891773 , 0.96366276, 0.38344152,
0.79172504, 0.52889492, 0.56804456, 0.92559664, 0.07103606,
0.0871293 ])
(Pdb) p fractional_indices
array([ 0. , 13.83351839, 27.66703678, 41.50055518,
55.33407357, 69.16759196, 83.00111035, 96.83462875,
110.66814714, 124.50166553, 138.33518392, 152.16870232,
166.00222071, 179.8357391 , 193.66925749, 207.50277589])
i'm struggling .. i'm going to skip into the fourier.py data
4 def create_freq2time(freq_rate, time_rate, freq_count, time_count):
5 freqs = np.fft.fftfreq(freq_count)
6 offsets = np.arange(freq_count) * freq_rate / time_rate
7 -> mat = np.exp(2j * np.pi * np.outer(freqs, offsets))
8 return mat / freq_count # scaled to match numpy convention
(Pdb) p freq_rate / time_rate
0.07228818957167302
(Pdb) p offsets
array([0. , 0.07228819, 0.14457638, 0.21686457, 0.28915276,
0.36144095, 0.43372914, 0.50601733, 0.57830552, 0.65059371,
0.7228819 , 0.79517009, 0.86745827, 0.93974646, 1.01203465,
1.08432284])
huh. it's using the old shorter offsets
(Pdb) p freq_rate, time_rate
(1.1566110331467683, 16)
the rates are samples / unit, I think. time here is recording, and
freq is waveform.
so it's saying the recording goes at 16 samples / unit . the unit must
be the whole recoridng.
the waveform frequency would then be 16 / max_period * 16, I guess.
i'm just passing max_period.
i decided 1 recording sample is 1 time unit which simplifies the
expressions. waveform_rate = waveform_N / max_period. recording_rate =
1
the offsets in create_freq2time are now the same as the fractional
indices in the sampler.
0852
here's [two rows of] the resulting matrix before it's scaled. these
would be the DC frequency multipliers, and then the 1st frequency's
multipliers:
(Pdb) p mat[:2]
array([[ 1. +0.j , 1. +0.j ,
1. +0.j , 1. +0.j ,
1. +0.j , 1. +0.j ,
1. +0.j , 1. +0.j ,
1. +0.j , 1. +0.j ,
1. +0.j , 1. +0.j ,
1. +0.j , 1. +0.j ,
1. +0.j , 1. +0.j ],
[ 1. +0.j , 0.65940045-0.75179189j,
-0.13038209-0.99146382j, -0.83134847-0.55575149j,
-0.96600102+0.25853825j, -0.44261455+0.89671197j,
0.38228055+0.92404631j, 0.94676649+0.32192113j,
0.86631595-0.49949643j, 0.19573177-0.98065747j,
-0.60818472-0.79379553j, -0.99780632-0.06620079j,
-0.70772316+0.70648987j, 0.06446038+0.99792027j,
0.79273357+0.60956828j, 0.98099736-0.19402106j]])
as i do this i find earlier assertions i can add that simplify the problem.
0854
(Pdb) n
> /shared/src/scratch/test2_upsamplish.py(21)<module>()
-> waveform_freq_2_recording_time =
fourier.create_freq2time(waveform_rate, recording_rate, waveform_N,
recording_N)
(Pdb) n
> /shared/src/scratch/test2_upsamplish.py(22)<module>()
-> assert np.allclose(np.fft.fft(waveform) @
waveform_freq_2_recording_time, recording)
(Pdb) n
> /shared/src/scratch/test2_upsamplish.py(23)<module>()
-> waveform_freq_reconstructed =
np.linalg.solve(waveform_freq_2_recording_time, recording)
It passed the first assertion. The matrix returned from fourier.py
produces the same sampled recording as the sampler function. So it's
all logical errors in running the test.
0855
