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
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