Audio & DSP

Python pathway

Programming Foundations / Practice rooms / Track curriculum and enrollment

1. Signals & Sampling

   Sound is a continuous pressure wave, but a computer can only hold a list of numbers. This project builds the bridge: generate the basic waveforms by hand, sample them at a chosen rate, and confront the two facts that govern all of digital audio, aliasing above the Nyquist frequency and the quantization noise of finite bit depth. Everything later in the track is built on these samples.

   • Generating Signals: 5 lessons
   • Waveform Shapes: 5 lessons
   • Sampling & Aliasing: 5 lessons
   • Quantization: 5 lessons
   • Amplitude & Levels: 5 lessons

2. Synthesis

   A synthesizer turns numbers into notes. This project builds the pieces of a voice: the ADSR envelope that shapes a note's loudness over time, additive synthesis that stacks harmonics into rich tones, amplitude and frequency modulation, the wavetable oscillator at the heart of most digital synths, and the mixing that lets many notes sound at once. By the end you can synthesize a chord from scratch.

   • Envelopes: 5 lessons
   • Additive Synthesis: 5 lessons
   • Modulation Synthesis: 5 lessons
   • Wavetable Oscillators: 5 lessons
   • Polyphony & Mixing: 5 lessons

3. The Fourier Transform

   Every signal is a sum of sinusoids, and the Fourier transform finds them. This project builds the Discrete Fourier Transform straight from its definition, reads off the magnitude and phase of each frequency bin, inverts the transform to get the signal back, and finally implements the Fast Fourier Transform, the divide-and-conquer algorithm that makes all of modern spectral audio possible. You will never call np.fft the same way again.

   • The DFT: 5 lessons
   • Magnitude & Phase: 5 lessons
   • The Inverse Transform: 5 lessons
   • The Fast Fourier Transform: 5 lessons
   • Reading a Spectrum: 5 lessons

4. Spectral Analysis

   A single FFT of a whole song is useless: it tells you which frequencies appear, but not when. Real analysis chops the signal into short overlapping frames, tapers each with a window to tame spectral leakage, and transforms them one at a time. This project builds the windows, the framing, the Short-Time Fourier Transform and the spectrogram it produces, and the parabolic interpolation that pinpoints a peak between bins.

   • Window Functions: 5 lessons
   • Framing: 5 lessons
   • The STFT & Spectrogram: 5 lessons
   • Peak Interpolation: 5 lessons
   • Analyzing a Tone: 5 lessons

5. Convolution & FIR Filters

   A filter shapes which frequencies pass through, and convolution is the operation that applies it. This project builds convolution from its definition, then designs Finite Impulse Response filters: the moving average, the windowed-sinc low-pass that is the workhorse of audio, high-pass by spectral inversion, and band-pass by cascading. You will compute a filter's frequency response and see exactly what it does to a spectrum.

   • Convolution: 5 lessons
   • FIR Basics: 5 lessons
   • Windowed-Sinc Design: 5 lessons
   • Frequency Response: 5 lessons
   • Filtering in Practice: 5 lessons

6. IIR Filters

   Where a FIR filter only looks at past inputs, an IIR filter feeds its own past outputs back in. That feedback buys steep filtering with very few coefficients, at the cost of possible instability. This project builds one-pole smoothers, the general difference equation, the second-order biquad that is the building block of every parametric equalizer, the RBJ cookbook coefficients, and the pole-zero analysis that tells you whether a filter will sing or blow up.

   • One-Pole Filters: 5 lessons
   • The Difference Equation: 5 lessons
   • The Biquad: 5 lessons
   • Poles, Zeros & Stability: 5 lessons
   • Building an Equalizer: 5 lessons

7. Audio Effects

   Now make it sound good. This project builds the effects rack: delay and feedback echo, the Schroeder reverb that stacks comb and allpass filters into a sense of space, the modulation effects (chorus, flanger, vibrato) that all come from one fractionally-interpolated delay line, distortion by waveshaping, and the dynamics processors (noise gate, envelope follower, compressor) that control loudness. These are the boxes on every guitarist's pedalboard and every mixing engineer's channel strip.

   • Delay & Echo: 5 lessons
   • Reverb: 5 lessons
   • Modulation Effects: 5 lessons
   • Distortion: 5 lessons
   • Dynamics: 5 lessons

8. Pitch & Time

   How does a tuner know the note, and how does a DAW change a singer's pitch without changing the tempo? This project answers both. It detects pitch in the time domain with zero-crossings and autocorrelation (the YIN idea), resamples to shift pitch, overlap-adds frames to stretch time independently of pitch, and maps frequencies onto the musical scale of notes and cents.

   • Zero-Crossing Analysis: 5 lessons
   • Autocorrelation Pitch: 5 lessons
   • Resampling: 5 lessons
   • Time Stretching: 5 lessons
   • Musical Pitch: 5 lessons

9. Features & Coding

   Machines do not listen to waveforms; they listen to features. This project builds the descriptors that drive speech recognition, music tagging, and audio codecs: loudness measures, the spectral-shape features (centroid, rolloff, flux) that capture timbre, the perceptual mel scale and its triangular filterbank, mu-law companding that squeezes audio into fewer bits, and onset detection that finds where the beats fall.

   • Loudness Features: 5 lessons
   • Spectral Shape: 5 lessons
   • Perceptual Scales: 5 lessons
   • Companding: 5 lessons
   • Onset Detection: 5 lessons

10. Capstone: A Subtractive Synthesizer

    Everything comes together as an instrument. A subtractive synth starts with a harmonically-rich oscillator, carves it with a filter, shapes its loudness with an ADSR envelope, and sweetens it through effects. This capstone builds that signal chain end to end, wires it into a voice that plays a MIDI note, renders a melody, and proves it works by detecting the pitch back out of the synthesized sound. You will have built a real synthesizer from first principles.

    • The Oscillator: 5 lessons
    • The Filter: 5 lessons
    • The Amplifier: 5 lessons
    • The Effects Send: 5 lessons
    • The Instrument: 5 lessons