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DSP Explorables
Interactive explanations of signal-processing ideas that are hard to get from equations and static textbook figures alone. Poke at them with your own audio.
Explorables
Section titled “Explorables”The Fourier transformFrom spinning arrows and Euler's identity to correlation, orthogonality, the DFT, epicycles and the FFT's butterflies.
Sampling and reconstructionLollipops, aliasing you can hear, the sampling theorem, rebuilding a signal exactly with sincs, and quantisation and dither.
Changing the sample rateDecimation and interpolation, images and aliases, polyphase filters for 44.1 ↔ 48 kHz, and how a stream of single bits can beat a CD.
Inside an MP3 encoderRecord a few seconds of audio and follow it through framing, the polyphase filterbank, the MDCT, the psychoacoustic model and bit allocation.
Pitch detectionThe missing fundamental, why the obvious methods fail, autocorrelation and octave errors, YIN step by step, the cepstrum, and a live tuner.
Pitch shifting and time stretchingA sampler playing one note at any pitch, the chipmunk problem, overlap-add, WSOLA, PSOLA, the phase vocoder, formants, and pitch correction.
Low-bitrate voice codingFrom 64 kbit/s μ-law to a working 8 kbit/s CELP coder: prediction, Levinson–Durbin, the residual, a vocoder, analysis by synthesis and line spectral pairs.
Finding signals below the noiseThresholds, averaging and correlation, the matched filter and why it's optimal, chirps and codes, spread spectrum and GPS, detection theory, and your own echo.
Modulation, part 1: putting a signal on a carrierMultiplying by a carrier and the receiver's phase problem, AM, I/Q signals, the Hilbert transform as a 90° all-pass filter, single sideband, FM, and a software-defined radio.
Modulation, part 2: sending bits over a real channelBPSK and the matched filter, QPSK and QAM, Gray coding, pulse shaping and eye diagrams, timing and carrier recovery, echoes and equalisers, OFDM, and a live acoustic modem.
Error-correcting codesRepetition, parity and CRCs, Hamming codes, distance and a fair comparison, interleaving, Reed–Solomon on a scratched recording, the Viterbi algorithm, soft decisions, and a coded modem.
Designing FIR filtersFrom a moving average to Parks–McClellan: frequency response, the Gibbs phenomenon, windows, Kaiser's formulas and equiripple design.
Exploring harmonicsWhy square waves come out of real equipment with ripple and a tilt: band-limiting and Gibbs, ringing before and after edges, phase, AC coupling, EQ, distortion and slew rate.
Designing IIR filtersFeedback, poles and zeros you can drag, biquads, the bilinear transform, Butterworth to elliptic, and the price in phase.