delays.lib
This library contains a collection of delay functions. Its official prefix is de.
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 samplesd: 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 samplesd: 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 samplesit: interpolation time (in samples), for example 1024d: the delay length in samples (float)
(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"
Reference
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 samplesd: 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.
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.
(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.
Reference
(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 4is the order of the Thiran interpolation filter (constant numerical expression), and the delay argument is at leastN-1/2. First-order:dat least 0.5, second-order:dat least 1.5, third-order:dat least 2.5, fourth-order:dat least 3.5.n: the max delay length in samplesd: 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).