Notes on exercise E6 of UPF SMC's Digital Signal Processing for Sound and Music: the harmonic model constrains every sinusoidal track to an integer multiple of a fundamental frequency f0, and the TWM algorithm finds f0 by comparing predicted harmonics with measured peaks in both directions. Four tasks: tracking only the melody's f0 in a cello recording where two strings sound at once, cutting a saxophone phrase into notes with the standard deviation of f0, measuring how far piano harmonics drift from integer multiples, and adding sub-harmonic candidates and Fletcher's formula to TWM. The figures are interactive animations.

DJI Mimo's phone export was too slow, so I spent a day with Claude Code rebuilding Mimo's color restore, HDR and beauty filter on the Mac as osmohdr, an open-source GPU-accelerated tool, plus a wide-angle correction attempt I dropped because it cost too much image quality.

Notes on exercise E5 of UPF SMC's Digital Signal Processing for Sound and Music: finding peaks in a spectrum, placing a peak between bins with a parabola, and connecting the peaks of successive frames into tracks, which is the sinusoidal model. Four tasks: getting the frequency error of a sinusoid below 0.05 Hz, tracking two chirps 40 Hz apart, tracking a sinusoid 500 times weaker than another, and choosing parameters for a complex signal. Also documents a problem in the current smstools sineModelAnal and a way around it.

Notes on exercise E4 of UPF SMC's Digital Signal Processing for Sound and Music, starting from the seam problem left at the end of E3: what a window is, how the spectrum takes the window's shape after windowing, main lobe and side lobes, zero-padding, cutting a sound into frames for the short-time Fourier transform and the spectrogram, and then the four tasks: extracting a window's main lobe, the error of STFT analysis followed by synthesis, band-wise energy envelopes, and finding piano note onsets from the difference in energy between neighbouring frames.

Notes on exercise E3 of UPF SMC's Digital Signal Processing for Sound and Music, part one: a 440 Hz cosine reads as 430.66 Hz, which leads to bin spacing, the leakage caused by a frame that does not hold a whole number of turns, the seam where the frame wraps around, and why the frame length for two sinusoids is the least common multiple of their periods. The figures are interactive animations.