Lesson 30 · A delay echo - Build a WAV/PCM Toolkit

A delay echo

A delay effect adds a quieter, time-shifted copy of a signal to itself, producing an echo. It is your first effect that reaches back in time, and it reuses mixing's clamp. Today you build it.

The goal

Add a delayed, attenuated copy of a signal to itself, clamping the sum.

Start here - the target

TO DO

Scenario: A delay adds an attenuated echo after a fixed lag

Giventhe signal [10000, 0, 0, 0], a delay of 2 samples, and a decay of 0.5, with out[n] = clamp(in[n] + round(decay*in[n-delay]))

Whenthe delay is applied

Thenthe result is [10000, 0, 5000, 0] - the echo of the first sample lands 2 positions later at half level

Andfor [30000, 0, 30000, 0] the echoed sample 30000 + 0.5*30000 = 45000 clamps to 32767

Background

A delay is the simplest time-based effect: for each sample it adds a copy of an earlier sample, attenuated by a decay factor, producing an audible echo. The lag sets how far back (how long until the echo), and decay sets how much quieter the echo is. The rule is out[n] = in[n] + decay * in[n-lag], and for the first lag samples there is no earlier sample to fetch, so they pass through untouched.

With lag 2 and decay 0.5, the lone 10000 at index 0 reappears at half level, 5000, at index 2 - a single slap-back echo. Because you are summing two signals, the result can exceed the range exactly like mixing, so you reuse clampInt16: 30000 + 0.5*30000 = 45000 clamps to 32767 rather than wrapping. (Feeding the output back in instead of the input would give a repeating echo - feedback delay - a natural extension.) This completes the toolkit; the capstone puts every piece to work at once.

Make it work

func delay(in []int, lag int, decay float64) []int {
  out := make([]int, len(in))
  for n := range in {
    v := in[n]
    if n >= lag {
      v += int(math.Round(decay * float64(in[n-lag])))   // add the echo
    }
    out[n] = clampInt16(v)
  }
  return out
}

CheckpointDONE

You can apply a delay echo. The synthesis toolkit is complete; commit and stop here.