delays.lib

Delays library. Its official prefix is de.

This library provides reusable building blocks for delay-based processing: single and multi-tap delays, fractional delays and utilities for echo and spatial effects.

The Delays library is organized into 4 sections:

References

Basic Delay Functions

(de.)delay

Simple d samples delay where n is the maximum delay length as a number of samples. Unlike the @ delay operator, here the delay signal d is explicitly bounded to the interval [0..n]. The consequence is that delay will compile even if the interval of d can't be computed by the compiler. delay is a standard Faust function.

Usage

_ : delay(n,d) : _

Where:

  • n: the max delay length in samples
  • d: the delay length in samples (integer)

Test

de = library("delays.lib");
os = library("oscillators.lib");
delay_test = os.osc(440) : de.delay(44100, 22050);

TODO: add MBH np2

(de.)fdelay

Simple d samples fractional delay based on 2 interpolated delay lines where n is the maximum delay length as a number of samples.

fdelay is a standard Faust function.

Usage

_ : fdelay(n,d) : _

Where:

  • n: the max delay length in samples
  • d: the delay length in samples (float)

Test

de = library("delays.lib");
os = library("oscillators.lib");
fdelay_test = os.osc(440) : de.fdelay(44100, 22050.5);

(de.)sdelay

s(mooth)delay: a mono delay that doesn't click and doesn't transpose when the delay time is changed.

Usage

_ : sdelay(n,it,d) : _

Where:

  • n: the max delay length in samples
  • it: interpolation time (in samples), for example 1024
  • d: the delay length in samples (float)

Test

de = library("delays.lib");
os = library("oscillators.lib");
sdelay_test = os.osc(440) : de.sdelay(44100, 1024, 22050.5);

(de.)prime_power_delays

Prime Power Delay Line Lengths.

Usage

si.bus(N) : prime_power_delays(N,pathmin,pathmax) : si.bus(N);

Where:

  • N: positive integer up to 16 (for higher powers of 2, extend 'primes' array below)
  • pathmin: minimum acoustic ray length in the reverberator (in meters)
  • pathmax: maximum acoustic ray length (meters) - think "room size"

Test

de = library("delays.lib");
prime_power_delays_test = de.prime_power_delays(4, 1, 10);

References

Lagrange Interpolation

(de.)fdelaylti and (de.)fdelayltv

Fractional delay line using Lagrange interpolation.

Usage

_ : fdelaylt[i|v](N, n, d) : _

Where:

  • N=1,2,3,... is the order of the Lagrange interpolation polynomial (constant numerical expression)
  • n: the max delay length in samples
  • d: the delay length in samples

fdelaylti is most efficient, but designed for constant/slowly-varying delay. fdelayltv is more expensive and more robust when the delay varies rapidly.

Note: the requested delay should not be less than (N-1)/2.

Test

de = library("delays.lib");
os = library("oscillators.lib");
fdelaylti_test = os.osc(440) : de.fdelaylti(3, 44100, 22050.5);
fdelayltv_test = os.osc(440) : de.fdelayltv(3, 44100, 22050.5);

References

(de.)fdelay[N]

For convenience, fdelay1, fdelay2, fdelay3, fdelay4, fdelay5 are also available where N is the order of the interpolation, built using fdelayltv.

Thiran Allpass Interpolation

Thiran Allpass Interpolation.

References

(de.)fdelay[N]a

Delay lines interpolated using Thiran allpass interpolation.

Usage

_ : fdelay[N]a(n, d) : _

(exactly like fdelay)

Where:

  • N=1,2,3, or 4 is the order of the Thiran interpolation filter (constant numerical expression), and the delay argument is at least N-1/2. First-order: d at least 0.5, second-order: d at least 1.5, third-order: d at least 2.5, fourth-order: d at least 3.5.
  • n: the max delay length in samples
  • d: the delay length in samples

Test

de = library("delays.lib");
os = library("oscillators.lib");
fdelay2a_test = os.osc(440) : de.fdelay2a(44100, 22050.5);

Note

The interpolated delay should not be less than N-1/2. (The allpass delay ranges from N-1/2 to N+1/2). This constraint can be alleviated by altering the code, but be aware that allpass filters approach zero delay by means of pole-zero cancellations.

Delay arguments too small will produce an UNSTABLE allpass!

Because allpass interpolation is recursive, it is not as robust as Lagrange interpolation under time-varying conditions (you may hear clicks when changing the delay rapidly).

Others

(de.)multiTapSincDelay

Variable delay line using multi-tap sinc interpolation.

This function implements a continuously variable delay line by superposing (2K+2) auxiliary delayed signals whose positions and gains are determined by a sinc-based interpolation method. It extends the traditional crossfade delay technique to significantly reduce spectral coloration artifacts, which are problematic in applications like Wave Field Synthesis (WFS) and auralization.

Operation:

  • If tau1 and tau2 are very close (|tau2 - tau1| ≈ 0), a simple fixed fractional delay is applied

  • Otherwise, a variable delay is synthesized by:

    • Computing (2K+2) taps symmetrically distributed around tau1 and tau2
    • Applying sinc-based weighting to each tap, based on its offset from the target interpolated delay tau
    • Summing all the weighted taps to produce the output

Features:

  • Smooth delay variation without introducing Doppler pitch shifts
  • Significant reduction of comb-filter coloration compared to classical crossfading
  • Switching between fixed and variable delay modes to ensure stability

Usage

_ : multiTapSincDelay(K, MaxDelay, tau1, tau2, alpha) : _

Where:

  • K (integer): number of auxiliary tap pairs (a constant numerical expression). Total number of taps = 2*K + 2
  • MaxDelay: maximum allowable delay in samples (buffer size)
  • tau1: initial delay in samples (can be fractional)
  • tau2: target delay in samples (can be fractional)
  • alpha: interpolation factor between tau1 and tau2 (in [0,1] with 0 = tau1, 1 = tau2)

Test

de = library("delays.lib");
os = library("oscillators.lib");
multiTapSincDelay_test = os.osc(440) : de.multiTapSincDelay(2, 4096, 1024.0, 1536.0, 0.5);

References