5a.
0:00 random walks
9:00 return to voice-score patch
10:00 principal component analysis (PCA) on random walks
17:00 graphs of the first 4 components of random walk samples
24:00 same with random walks adjusted to sum to zero gives cosine transform
28:30 why we don't use cosine transform to analyze time series like audio
39:00 bark cepstrum doesn't treat phase the same way as Fourier spectra
44:00 Bark cepstrum low-order coefficients as brutal way to characterize timbre
45:00 linear prediction (LPC) as a similar problem to PCA
46:00 LPC as vocal analysis technique based on a simple vocal model
47:00 3 resonant filters in series rewritten as a 6-pole recursive (IIR) filter
50:00 recursive expression for IIR filter
55:00 LPC as a power-minimization problem like PCA but simpler
57:00 abstract linear prediction problem (not necessarily a time series)
1:09:00 linear prediction error as a parabola
1:10:30 reduce problem to one predictor
1:13:00 vertex of the parabola - "-b/(2a)" from high school algebra
5b.
0:00 LPC on audio, testing on bell recording
14:00 implementation in Julia script
17:00 in covariance method, get a symmetric (but not Toeplitz) matrix
24:00 ideally we'd just grab the decay portion of the filters
40:00 effect of sample rate on LPC effectiveness
41:00 LPC gives an all-pole filter, no zeros, which doesn't model nasal passage
44:00 Pitch. mixedness (non-independence) of timbre and pitch
44:45 time-domain notion of pitch as quasi-periodicity vs. spectrum
49:40 the YIN pitch estimation algorithm
1:03:30 frequency-domain (Terhardt) approach to pitch estimation
1:06:00 pitch spectrum