# delays.lib

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

## 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)

### (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)

### (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)

## 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.

### (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.

### (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

#### 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).