synthesizer-core-0.6: Audio signal processing coded in Haskell: Low level part

Synthesizer.Interpolation.Module

Description

Special interpolations defined in terms of Module operations.

Synopsis

# Documentation

data T t y Source

interpolation as needed for resampling

constant :: T t ySource

Consider the signal to be piecewise constant, where the leading value is used for filling the interval [0,1).

linear :: C t y => T t ySource

Consider the signal to be piecewise linear.

cubic :: (C t, C t y) => T t ySource

Consider the signal to be piecewise cubic, with smooth connections at the nodes. It uses a cubic curve which has node values x0 at 0 and x1 at 1 and derivatives (x1-xm1)2 and (x2-x0)2, respectively. You can see how it works if you evaluate the expression for t=0 and t=1 as well as the derivative at these points.

cubicAlt :: (C t, C t y) => T t ySource

The interpolators for module operations do not simply compute a straight linear combination of some vectors. Instead they add then scale, then add again, and so on. This is efficient whenever scaling and addition is cheap. In this case they might save multiplications. I can't say much about numeric cancellations, however.

piecewise :: C t y => Int -> [t -> t] -> T t ySource

piecewiseLinear :: C t y => T t ySource

piecewiseCubic :: (C t, C t y) => T t ySource

Arguments

 :: C t y => (Int, Int) `(left extent, right extent)`, e.g. `(1,1)` for linear hat -> (t -> t) -> T t y

with this wrapper you can use the collection of interpolating functions from Donadio's DSP library