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