synthesizer-0.0.3: Audio signal processing coded in Haskell Source code Contents Index

Synthesizer.Plain.Interpolation

Contents Interpolation with various padding methods Interpolation of multiple values with various padding methods Interpolation of multiple values with various padding methods All-in-one interpolation functions Different kinds of interpolation Hard-wired interpolations Interpolation based on piecewise defined functions Interpolation based on arbitrary functions Helper functions

Description

ToDo: use AffineSpace instead of Module for the particular interpolation types, since affine combinations assert reconstruction of constant functions. They are more natural for interpolation of internal control parameters. However, how can cubic interpolation expressed by affine combinations without divisions?

Synopsis

data T t y = Cons { number :: Int offset :: Int func :: t -> T y -> y } zeroPad :: C t => (T t y -> t -> T y -> a) -> y -> T t y -> t -> T y -> a constantPad :: C t => (T t y -> t -> T y -> a) -> T t y -> t -> T y -> a cyclicPad :: C t => (T t y -> t -> T y -> a) -> T t y -> t -> T y -> a extrapolationPad :: C t => (T t y -> t -> T y -> a) -> T t y -> t -> T y -> a skip :: C t => T t y -> (t, T y) -> (t, T y) single :: C t => T t y -> t -> T y -> y singleRec :: (Ord t, C t) => T t y -> t -> T y -> y multiRelative :: C t => T t y -> t -> T y -> T t -> T y multiRelativeZeroPad :: C t => y -> T t y -> t -> T t -> T y -> T y multiRelativeConstantPad :: C t => T t y -> t -> T t -> T y -> T y multiRelativeCyclicPad :: C t => T t y -> t -> T t -> T y -> T y multiRelativeExtrapolationPad :: C t => T t y -> t -> T t -> T y -> T y multiRelativeZeroPadConstant :: (C t, C y) => t -> T t -> T y -> T y multiRelativeZeroPadLinear :: (C t, C t y) => t -> T t -> T y -> T y multiRelativeZeroPadCubic :: (C t, C t y) => t -> T t -> T y -> T y data PrefixReader y a = PrefixReader Int (StateT (T y) Maybe a) getNode :: PrefixReader y y fromPrefixReader :: String -> Int -> PrefixReader y (t -> y) -> T t y constant :: T t y linear :: C t y => T t y cubic :: (C t, C t y) => T t y cubicAlt :: (C t, C t y) => T t y cubicHalf :: C t y => t -> y -> y -> y piecewise :: C t y => Int -> [t -> t] -> T t y piecewiseConstant :: C t y => T t y piecewiseLinear :: C t y => T t y piecewiseCubic :: (C t, C t y) => T t y function :: C t y => (Int, Int) -> (t -> t) -> T t y minLength :: Int -> T y -> Bool

Documentation

data T t y Source

interpolation as needed for resampling Constructors Cons number :: Int offset :: Int func :: t -> T y -> y

Interpolation with various padding methods

zeroPad :: C t => (T t y -> t -> T y -> a) -> y -> T t y -> t -> T y -> a Source

constantPad :: C t => (T t y -> t -> T y -> a) -> T t y -> t -> T y -> a Source

cyclicPad :: C t => (T t y -> t -> T y -> a) -> T t y -> t -> T y -> a Source

Only for finite input signals.

extrapolationPad :: C t => (T t y -> t -> T y -> a) -> T t y -> t -> T y -> a Source

The extrapolation may miss some of the first and some of the last points

Interpolation of multiple values with various padding methods

skip :: C t => T t y -> (t, T y) -> (t, T y) Source

single :: C t => T t y -> t -> T y -> y Source

singleRec :: (Ord t, C t) => T t y -> t -> T y -> y Source

alternative implementation of single

Interpolation of multiple values with various padding methods

multiRelative :: C t => T t y -> t -> T y -> T t -> T y Source

All values of frequency control must be non-negative.

multiRelativeZeroPad :: C t => y -> T t y -> t -> T t -> T y -> T y Source

multiRelativeConstantPad :: C t => T t y -> t -> T t -> T y -> T y Source

multiRelativeCyclicPad :: C t => T t y -> t -> T t -> T y -> T y Source

multiRelativeExtrapolationPad :: C t => T t y -> t -> T t -> T y -> T y Source

The extrapolation may miss some of the first and some of the last points

All-in-one interpolation functions

multiRelativeZeroPadConstant :: (C t, C y) => t -> T t -> T y -> T y Source

multiRelativeZeroPadLinear :: (C t, C t y) => t -> T t -> T y -> T y Source

multiRelativeZeroPadCubic :: (C t, C t y) => t -> T t -> T y -> T y Source

Different kinds of interpolation

Hard-wired interpolations

data PrefixReader y a Source

Constructors PrefixReader Int (StateT (T y) Maybe a) Instances Functor (PrefixReader y) Applicative (PrefixReader y)

getNode :: PrefixReader y y Source

fromPrefixReader :: String -> Int -> PrefixReader y (t -> y) -> T t y Source

constant :: T t y Source

Consider the signal to be piecewise constant.

linear :: C t y => T t y Source

Consider the signal to be piecewise linear.

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

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 y Source

cubicHalf :: C t y => t -> y -> y -> y Source

Interpolation based on piecewise defined functions

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

piecewiseConstant :: C t y => T t y Source

piecewiseLinear :: C t y => T t y Source

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

Interpolation based on arbitrary functions

function Source

:: 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

Helper functions

minLength :: Int -> T y -> Bool Source

Test if a list has at least n elements make sure that n is non-negative

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