Synthesis Theory I: Topics

Sinewaves and Additive Synthesis

• Sound Decomposition
• Mathematical Definition of Sinewaves
• Physical Properties of Sinewaves
• Perceptual Properties of Sinewaves
  • Physiology of Hearing
  • Decibels
  • Frequency Range of Hearing
  • Fletcher-Munsen Equal-Loudness Curves
  • Phase
• Timbre
• Additive Synthesis

Soundfiles and Digital Recording

• Shannon Sampling Theorem
• Quantization
• Sound File Formats
• Recording your own soundfiles
• Sound Editing
• Basic Fourier Theory

Wavetable Synthesis

• Wavetable Concept and Origins
• Sampling Synthesis: How Samplers Work
• Granular Synthesis

Subtractive Synthesis and Linear Filtering

• Noise
• Linear Filtering Components: Addition, Scaling, Delay
• Lowpass/Highpass Filter
• Resonant Filter
• Filter design using the Z-plane and Z-transform
  • Poles and Zeros
  • Mathematics of Filter Design
• Flange Filtering
• Comb Filter
• Allpass Filter
• Reverberation

Physical Modeling Synthesis

• Karplus-Strong Dynamic Wavetable Algorithm
• Delay Lines and String Modeling

Non-Linear Synthesis

• Ring Modulation
• FM Synthesis
• Waveshaping Synthesis