270b-01-mar28.mp4: Meeting 1, March 28, 2022 0:00 This course is about signal analysis, not cognitive science as advertised 5:00 about the sonic challenges 6:00 first sonic challenge: the call of the white bellbird 21:30 short-time Fourier analysis (STFT) 26:00 tools used in this course: Pd, Audacity, Julia 29:00 storing a sinusoid in an array in Pd 33:30 classical envelope follower: rectify and low-pass filter 36:30 phase of a sinusoid 40:00 phase quadrature 42:00 complex sinusoid as real sinusoid pair 44:30 magnitude of a complex sinusoid 47:30 the hilbert~ object 50:00 measuring the magnitude of a real sinusoid using hilbert~ 54:00 sinusoids in nature: time-varying frequency and magnitude 56:00 ring (amplitude) modulation to change frequency of a sinusoid 58:30 aliasing a frequency to almost zero 59:30 using phase quadrature to modulate an oscillator 1:01:30 low-pass filtering the modulated sinusoid 1:02:00 measuring the magnitude of the sinusoid 1:04:00 reaction time of magnitude measurement 1:05:00 trade-off, stability versus reaction speed 270b-02-mar30.mp4: Meeting 2, March 30, 2022 1:00 finding and loading the example patches from classes. Some Pd basics. 5:30 complex-mpy~ abstraction 7:00 ampliude detection from previous class understood as a frequency shift 14:30 real and complex sinusoids. Real sinusoid is sum of two complex ones 21:00 measuring amplitude and phase of a complex sinusoid 27:00 single sideband modulation as product of complex sinusoids 32:00 x/y plot using Pd of a complex sinusoid. 33:00 Positive frequency sinusoids travel counter-clockwise in complex plane 40:00 Measuring phase differences between neighboring sinusoids 42:30 complex conjugate negates frequencies of sinusoids 43:30 phase difference3 between an incoming sinusoid and a known sinusoid 51:00 analysing complex spectra (tones with more than one partial) 56:00 spectrum of frequency-shifted complex sinusoid making 6 components visible 1:01:00 low-pass filtering a sum of complex sinusoids 1:03:00 Fourier analysis of a periodic tone 1:08:00 Short-time Fourier transform 1:09:00 Window as a segment in time 1:13:00 windowing a non-periodic signal 1:15:00 trade-off between time and frequency resolution 270b-03-apr04.mp4: Meeting 3, April 4, 2022 0:00 terminology: DFT, FFT, STFT (short-time FT), WSTFT (windowed STFT) 4:00 windowing and window functions 6:00 magnitude spectrum of a sawtooth; discontinuities in waveforms 8:00 analyzing a sinusoid not tuned to window size 10:30 boxcar (rectangular) window function 12:00 continuous-time Fourier transform of a windowed sinusoid 13:00 total energy of a continuous-time signal 14:30 Hann window function in continuous time 21:30 Hann window in discrete time (patch example 5.hann-window.pd) 29:00 analyzing and playing the contents of a window as a periodic signal 39:00 windowed analysis of a constant signal. Main lobe and sidelobes 44:00 spectrum of a square wave 50:00 spectrum of the Hann window function and a Hann windowed sinusoid 57:00 derived boxcar window spectrum 1:03:00 sinx function 1:06:00 measuring the spectrum of a short square pulse (boxcar window function) 1:10:00 derived spectrum of Hann window 1:15:00 spectrum of Hann windowed sinusoid 1:17:00 superposition of two sinusoids 270b-04-apr06.mp4: Meeting 4, April 6, 2022 0:00 How the discrete Fourier transform (DFT) works 3:00 fundamental frequency is sample rate divided by N 10:30 complex-valued Fourier transform of a constant signal 12:00 formula for discrete-time Fourier transform (generalization of DFT) 20:00 normalizing the DFT 21:30 inverse DFT to recover original array 27:00 DFT as way to separate frequency ranges in a signal 32:00 freqency bins and Fourier analysis between bins 46:00 relationship between sinx function and Fourier transform of a sinusoid 49:30 Pd example patch: 64-point DFT of a sinusoid 56:00 changing the starting phase of the sinusoid 1:00:00 graph of analyzed waveform 1:09:00 how the FFT works 1:16:00 DFT as multiplication by a unitary matrix 270b-05-apr11.mp4: Meeting 5, April 11, 2022 1:30 Portnoff paper on WSTFTs; channels of transform are low-bandwidth signals 5:00 tail behavior of Hann window spectrum 9:30 Blackman-Harris window 15:00 zero-frequency bin as low-pass filter 20:00 output can be downsampled to a hop size of N/4 24:00 situation for bin 1 31:00 signal is multiplied by Hann window times complex exponential 34:30 alternating signs of consecutive bins when analyzing a sinuaoid 39:00 measured phase precesses for nonzero bins 48:00 analysis of sinusoid tuned to first bin, H=N/4 53:00 measuring frequency of a sinusoid using phase precession (phase vocoder) 54:00 multiple possible vaules of frequency separated by 1/H cycles per sample 59:00 aliased frequencies should differ by at least 4 bins so we need H <= N/4 1:05:00 analyzing complex sums of sinusoids 1:10:00 needed separation between sinusoids to resolve them 1:12:00 demonstration using Pd help window I02.Hann.window.pd 1:17:00 N=2038 at 48000: 23 Hz. per bin, 43 millisecond window. 270b-06-apr13.mp4: Meeting 6, April 13, 2022 0:00 the white bellbird analyzed and resynthesized 9:30 06.pvoc-squeezed-spect-graph.pd in class patches 18:00 peaks in bellbird spectrum 25:00 synthesizing a formant 29:00 pulse trains by waveshaping sinusoids 35:00 seeing between the bins in a Fourier analysis by zero padding 46:00 thought experiment: pinched windows and signal variations within windows 47:00 applying Hann window a posteriori by convolving window kernel 56:00 Peeters (ICMC 1999) - analyzing a chirp (swept sinusoid) 1:05:00 rate of frequency change adds to measured bandwidth in WSTFT [remaining videos not yet indexed.]