delays.lib

This library contains a collection of delay functions. Its official prefix is de.

Basic Delay Functions

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(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 as a number of samples (integer)

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(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 as a number of samples (float)

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(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,dt) : _

Where :

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

Lagrange Interpolation

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(de.)fdelaylti and (de.)fdelayltv

Fractional delay line using Lagrange interpolation.

Usage

_ : fdelaylt[i|v](order, maxdelay, delay, inputsignal) : _

Where order=1,2,3,... is the order of the Lagrange interpolation polynomial.

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 (order-1)/2.

References

• https://ccrma.stanford.edu/~jos/pasp/Lagrange_Interpolation.html
• fixed-delay case
• variable-delay case
• Timo I. Laakso et al., "Splitting the Unit Delay - Tools for Fractional Delay Filter Design", IEEE Signal Processing Magazine, vol. 13, no. 1, pp. 30-60, Jan 1996.
• Philippe Depalle and Stephan Tassart, "Fractional Delay Lines using Lagrange Interpolators", ICMC Proceedings, pp. 341-343, 1996.

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(de.)fdelay[n]

For convenience, fdelay1, fdelay2, fdelay3, fdelay4, fdelay5 are also available where n is the order of the interpolation.

Thiran Allpass Interpolation

Thiran Allpass Interpolation

Reference

• https://ccrma.stanford.edu/~jos/pasp/Thiran_Allpass_Interpolators.html

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(de.)fdelay[n]a

Delay lines interpolated using Thiran allpass interpolation.

Usage

_ : fdelay[N]a(maxdelay, delay, inputsignal) : _

(exactly like fdelay)

Where:

• N=1,2,3, or 4 is the order of the Thiran interpolation filter, and the delay argument is at least N - 1/2.

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. The delay range [N-1/2,N+1/2] is not optimal. What is?

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.)

First-order allpass interpolation, delay d in [0.5,1.5]