13.8 Summary

13.8 Summary#

  • Audio effects are filters used for creative purposes, typically ones that are not LTI, or that combine simpler filters in sophisticated topologies. A wet/dry mix blends the processed (wet) and unprocessed (dry) signals as \((1 - w) \cdot \mathbf{x} + w \cdot \mathbf{y}\), where a wet-to-dry ratio of \(\text{dB}\) decibels gives \(w = 1 / (1 + 10^{-\text{dB}/20})\).

  • A feedback delay line, \(y[n] = x[n] + g \cdot y[n - M]\), produces different effects depending on how \(\frac{f_s}{M}\) compares to \(20\) Hz: comb filtering for short delays, a delay effect for delays longer than \(50\) ms, and an echo for delays on the order of seconds.

  • A tapped delay line reads a delay line at a time-varying, fractional position, enabling variable delays. Flanging sweeps the short delay of a feedback delay line with a slow sinusoid, which sweeps its comb up and down in frequency. A sinusoidally varying delay also applies vibrato to its input, like FM synthesis.

  • A multitap delay line reads one delay line at several positions. Chorus mixes a sound with several copies, each with its own slowly varying delay of \(20\) to \(30\) ms.

  • An all-pass filter, \(y[n] = -g \cdot x[n] + x[n - M] + g \cdot y[n - M]\), produces echoes without coloring the sound. Schroeder’s reverberator simulates reverberation with four feedback delay lines in parallel and two all-pass filters in series, with gains set by the reverberation time \(T_{60}\).

  • Distortion is non-linear, so it creates new frequency content. Waveshaping passes each sample through a transfer function, \(y[n] = f(x[n])\), from hard and soft clipping to Chebyshev polynomials, which turn a sinusoid into its harmonics.

  • A compressor reduces dynamic range, by turning a signal down wherever its RMS amplitude exceeds a threshold, so that every \(R\) dB above the threshold becomes \(1\) dB. Side-chain compression measures the loudness of a different signal.

  • Localization relies on time differences, level differences, and spectral cues. Stereo preserves these cues with two channels. Panning places a mono sound between the channels, ideally with a constant-power law. A ping-pong delay bounces echoes between the channels, and a mid/side representation controls the width of a stereo sound.