UIUC MUS 102 Notes

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Course Overview

This course surveys computer music and audio digital signal processing (DSP) with an emphasis on spectral analysis/synthesis, psychoacoustics, physical and modal modeling, room acoustics, and modern modulation and cross-synthesis techniques. You will learn how sound is analyzed, represented, transformed, and resynthesized for music technology, alongside practical insights into human hearing and real-world audio systems.

Learning Outcomes

By the end, students should be able to:

• Explain core psychoacoustic concepts (critical bands/Bark scale, masking, place principle) and apply them to analysis and synthesis.
• Perform short-window (pitch-synchronous) and long-window spectral analysis, peak picking, and track partials; understand reassignment for sharpened time-frequency localization.
• Implement and compare additive, wavetable, BLIT/DSF, granular, AM/FM/SSB methods; reason about aliasing and bandlimiting.
• Apply cross-synthesis approaches (vocoder, LPC) and morphing between timbres.
• Model instruments and acoustics via digital waveguides, modal and kinetic models; reason about nonlinearity and parameterization.
• Analyze room acoustics (direct/early/late energy, critical distance, T60) and practical reverberation/convolution workflows.
• Understand audio I/O interfaces (I2S, AES3) and clocking at a block/bit level.

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Syllabus (Modules)

Organized by topic clusters so you can map to weeks as needed.

1) Psychoacoustics & Timbre

• Ear anatomy & place principle on the basilar membrane
• Critical bands / Bark scale; loudness and masking (spectral & temporal)
• What defines timbre (brightness, attack, etc.); multidimensional scaling notions

2) Time–Frequency Analysis

• Short-window, pitch-synchronous analysis: assumptions (monophonic, quasi-harmonic), window length vs. overlap, amplitude/phase tracking, phase-overflow correction
• Long-window (Kaiser/Fitz-Haken tuning): peak detection, parabolic interpolation (Serra & Smith), partial birth/death & “zipper” artifacts
• Reassignment spectrograms: center-of-gravity relocation to sharpen attacks and formants; computational shortcuts via STFT ratios

3) Additive & Wavetable Synthesis

• Additive resynthesis from tracked partials; envelopes for magnitude/phase
• Fixed-waveform spectral matching (basis spectra + time-varying envelopes)
• Multiple wavetables: least-squares/QR, orthogonalization; PCA for optimal bases; genetic search heuristics
• Supersaw detuning to mask aliasing / enrich spectra

4) Bandlimited Oscillation & Aliasing Control

• BLIT (bandlimited impulse train) and bipolar BLIT; numerical integration caveats
• DSF (Discrete Summation Formula): harmonic roll-off control (S parameter)
• Practical aliasing constraints vs. sampling rate, table size, and key-mapped tables

5) Modulation & Pitch Processing

• AM / Ring modulation (carrier/offset images), SSB via ±90° phasing
• FM spectral structure (Bessel-function sidebands, index control)
• Pitch shifting trade-offs (aliasing, envelope/attack changes); speech-specific zero-insertion vs. musical content

6) Cross-Synthesis & LPC

• Vocoder analysis banks driving timbre shaping
• LPC: linear prediction, residual/excitation, filter interpretation; speech-music cross-applications
• Morphing vs. cross-synthesis (contrast; when each is appropriate)

7) Physical & Modal Modeling

• Digital waveguides (traveling waves, delays, boundary filters), junction scattering, room/edge diffusion ideas
• Modal modeling (low-frequency modes; architectural acoustics focus), parameter estimation challenges
• Kinetic (finite-difference) approaches and stability/continuity considerations
• Handling nonlinearities (reed/bow mouthpiece lookup, waveshaping)

8) Room Acoustics & Reverberation

• Direct, early reflections, late diffuse field; critical distance
• T60 estimation & Sabine-type calculations; issues with position dependence and dynamic-range limits
• Energy decay integration and crossover points; low-frequency persistence
• Convolution for reverberation and body responses; occlusion/edge-diffusion approximations

9) Practical Spectral Resynthesis

• Envelope interpolation; phase/frequency handling under modulation
• Noise channels for high-frequency residuals; when/why phase alignment is unnecessary in musical reconstructions
• Computational concerns and artifact mitigation

10) Audio Interfaces & Clocking

• I2S (MCLK/LRCLK/SCLK roles; word framing), same-board constraints
• AES3 framing (subframes/frames/blocks), preambles (X/Y/Z), biphase mark and clock recovery

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Tools & Techniques You Should Be Comfortable With

• STFT/ISTFT with window/overlap choice; Kaiser/Hamming/Hann selection
• Peak picking & parabolic interpolation; partial tracking heuristics
• Using reassignment to improve TF localization
• Constructing bandlimited oscillators (BLIT/DSF) and diagnosing aliasing
• Building FM/AM/SSB blocks and reading their spectra
• Implementing simple LPC analysis–synthesis loops
• Designing waveguide building blocks and small modal banks
• Calculating T60/critical distance and doing simple room-IR convolution