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 samplesd
: the delay length as a number of 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 as a number of 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,dt) : _
Where :
n
: the max delay length in samplesit
: interpolation time (in samples) for example 1024dt
: delay time (in samples)
Lagrange Interpolation
(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.
(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
(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]