synthesizer-filter (empty) → 0.4
raw patch · 12 files changed
+1774/−0 lines, 12 filesdep +basedep +containersdep +numeric-preludesetup-changed
Dependencies added: base, containers, numeric-prelude, numeric-quest, synthesizer-core, transformers, utility-ht
Files
- LICENSE +674/−0
- Setup.lhs +3/−0
- src/Synthesizer/Filter/Basic.hs +60/−0
- src/Synthesizer/Filter/Composition.hs +150/−0
- src/Synthesizer/Filter/Example.hs +243/−0
- src/Synthesizer/Filter/Fix.hs +38/−0
- src/Synthesizer/Filter/Graph.hs +183/−0
- src/Synthesizer/Filter/Graphic.hs +7/−0
- src/Synthesizer/Filter/MonadFix.hs +44/−0
- src/Synthesizer/Filter/OneWay.hs +76/−0
- src/Synthesizer/Filter/TwoWay.hs +247/−0
- synthesizer-filter.cabal +49/−0
+ LICENSE view
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+ Setup.lhs view
@@ -0,0 +1,3 @@+#! /usr/bin/env runhaskell+> import Distribution.Simple+> main = defaultMain
+ src/Synthesizer/Filter/Basic.hs view
@@ -0,0 +1,60 @@+{-# LANGUAGE NoImplicitPrelude #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE FunctionalDependencies #-}+module Synthesizer.Filter.Basic where++import qualified Algebra.Transcendental as Trans+import qualified Algebra.Module as Module+import qualified Algebra.RealRing as RealRing+import qualified Number.Complex as Complex++import NumericPrelude.Numeric+import NumericPrelude.Base++{- ToDo:+ - support of data before time 0+ - the problem is that all past data has to be kept,+ the garbage collector can't flush it :-(+ - this means we will also need functions for plain lists,+ in this case we can't provide initial conditions to recursive filters+ - the question of initial conditions is especially problematic+ since for Graphs we have no explicit feed back+ where initial conditions can be plugged in+ - thus for two-way signal we must request the user+ to insert initial conditions in every loop of a Graph+ using the Past constructor+ - all of the following filter primitives in static and modulated form:+ - mask+ - integer delay+ - fractional delay+ - shall the fractional delay constructor store the interpolation type?+ (this discussion is similar to the one concerning+ initial conditions for recursive filters)+ - yes, because each delay may use a different interpolation type,+ if no fractional delay is used,+ no interpolation type needs to be specified+ - no, because the interpolation is only of interest for filter+ application not for the transfer function+ - Is there a way to avoid the multi-parameter type class?+ - Can we provide a class for lists (OneWay and TwoWay)+ that help implementing filters and filter networks?+ - The 'transferFunction' obviously does not depend on the signal list type.+ - 'transferFunction' should not be restricted to complex numbers.+ - For arguments of type 'Ratio (Polynomial Rational)'+ you could compute the transfer function in terms of a rational function.+-}++screw :: Trans.C a => a -> [Complex.T a]+screw w = iterate (Complex.cis w *) 1+++class Filter list filter | filter -> list where+ {-| Apply a filter to a signal. -}+ apply :: (RealRing.C t, Trans.C t,+ Module.C a v, Module.C a (list v)) =>+ filter t a v -> list v -> list v+ {-| Compute the complex amplification factor+ that is applied to the given frequency. -}+ transferFunction :: (Trans.C t, Module.C a t) =>+ filter t a v -> t -> Complex.T t
+ src/Synthesizer/Filter/Composition.hs view
@@ -0,0 +1,150 @@+{-# LANGUAGE NoImplicitPrelude #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE UndecidableInstances #-}+module Synthesizer.Filter.Composition where++import qualified Synthesizer.Filter.Basic as FilterBasic+import Synthesizer.Filter.Basic (Filter, apply, )++import qualified Algebra.Module as Module+import qualified Algebra.Transcendental as Trans+import qualified Algebra.RealRing as RealRing+import qualified Algebra.Field as Field+import qualified Algebra.Additive as Additive+import qualified Number.Complex as Complex++import Algebra.Additive ((+))++import NumericPrelude.Base+import NumericPrelude.Numeric++{- ToDo:+ - functions that build a FilterComposition for specific filters+ (1st order, universal, allpass, butterworth, chebyshev)+ - functions that turn physical filter parameters into+ internal ones+ - How can these function be combined?+ A function like+ [ FilterComposition v [m] ] -> FilterComposition v [[m]]+ is not satisfying, since the conversion function cannot rely+ that the structure of all FilterComposition v [m] is equal.+ If the list is empty the structure can't even be reconstructed.+-}++{-|+ This describes a generic filter with one input and one main output+ that consists of non-recursive and recursive parts.+ If you use Feedback, make sure that at least+ one of the filters of a circle includes a delay,+ otherwise the recursion will fail.+ The main output is used to glue different parts together.+ Additionally the functions 'apply' and 'transferFunction'+ provide the signals at every node of the network.+-}+data T filter t a v =+ Prim (filter t a v)+ {-^ a filter primitve -}+ | Serial [T filter t a v]+ {-^ serial chain of filters -}+ | Parallel [T filter t a v]+ {-^ filters working parallel, there output is mixed together -}+ | Feedback (T filter t a v) (T filter t a v)+ {-^ filter the signal in the forward direction and+ feed back the output signal filtered by the second filter -}++{-|+ This is the data structure is used for the results+ of 'apply' and 'transferFunction'.+ Each constructor corresponds to one of 'Filter.Composition.T'.+ By choosing only some of the outputs+ the lazy evaluation will content+ with applying the necessary filter steps, only.+-}+data Sockets s = Sockets {output :: s, socket :: SocketSpec s}++data SocketSpec s =+ Output+ | Multiplier [Sockets s]+ | Adder [Sockets s]+ | Loop (Sockets s) (Sockets s)++instance (Filter list filter) =>+ Filter (list) (T filter) where+{-+ apply :: (Module.C a v) =>+ FilterComposition a v -> TwoWayList v -> TwoWayList v+-}+ apply f x = output (applyMulti f x)+{-+ transferFunction :: (Trans.C b, Module.C a (Complex.T b)) =>+ T filter a v -> b -> (Complex.T b)+-}+ transferFunction f w = output (transferFunctionMulti f w)+++{-| Apply a filter network to a signal and keep the output of all nodes.+ Generic function that is wrapped by 'apply'. -}+applyMulti :: (RealRing.C t, Trans.C t,+ Module.C a v, Module.C a (list v), Filter list filter) =>+ T filter t a v -> list v -> Sockets (list v)+applyMulti (Prim f) x =+ Sockets (apply f x) Output+applyMulti (Serial fs) x =+ let sq = scanl (\(Sockets y _) -> flip applyMulti y) (Sockets x Output) fs+ in Sockets (output (last sq)) (Multiplier (tail sq))+applyMulti (Parallel fs) x =+ let socks = map (flip applyMulti x) fs+ y = foldr (Additive.+) zero (map output socks)+ in Sockets y (Adder socks)+{- the distinction between 'feed' and 'back'+ can be dropped in a more general net structure -}+applyMulti (Feedback feed back) x =+ let sockY@(Sockets y _) = applyMulti feed ((Additive.+) x z)+ sockZ@(Sockets z _) = applyMulti back y+ in Sockets y (Loop sockY sockZ)+++transferFunctionMulti ::+ (Trans.C t, Module.C a t, Filter list filter) =>+ T filter t a v -> t -> Sockets (Complex.T t)+transferFunctionMulti f w = tfAbsolutize 1 (tfRelative w f)++{-| Compute the transitivity for each part of the filter network.+ We must do this in such a relative manner to be able+ to compute feedback. -}+tfRelative ::+ (Trans.C t, Module.C a t, Filter list filter) =>+ t -> T filter t a v -> Sockets (Complex.T t)+tfRelative w (Prim f) =+ Sockets (FilterBasic.transferFunction f w) Output+tfRelative w (Serial fs) =+ let sq = map (tfRelative w) fs+ in Sockets (product (map output sq)) (Multiplier sq)+tfRelative w (Parallel fs) =+ let sq = map (tfRelative w) fs+ in Sockets (sum (map output sq)) (Adder sq)+tfRelative w (Feedback feed back) =+ let sockY = tfRelative w feed+ sockZ = tfRelative w back+ q = output sockY / (1 - output sockZ)+ in Sockets q (Loop sockY sockZ)+++{-| Make the results from 'tfRelative' absolute. -}+tfAbsolutize :: (Field.C a) => a -> Sockets a -> Sockets a+tfAbsolutize x (Sockets y spec) = Sockets (x*y)+ (case spec of+ (Multiplier socks) ->+ let sq = scanl (\(Sockets z _) -> tfAbsolutize z)+ (Sockets x Output) socks+ in Multiplier (tail sq)+ (Adder socks) ->+ let sq = map (tfAbsolutize x) socks+ in Adder sq+ (Loop feed back) ->+ let sockY = tfAbsolutize (x / (1 - output back)) feed+ sockZ = tfAbsolutize (output sockY) back+ -- it should be x*y == output sockY+ in Loop sockY sockZ+ Output -> spec)
+ src/Synthesizer/Filter/Example.hs view
@@ -0,0 +1,243 @@+{-# LANGUAGE NoImplicitPrelude #-}+module Synthesizer.Filter.Example where++import qualified Synthesizer.Filter.OneWay as OneWay+import qualified Synthesizer.Filter.TwoWay as TwoWay+import qualified Synthesizer.Filter.Composition as Composition+import qualified Synthesizer.Filter.Graph as Graph+import qualified Synthesizer.Plain.Interpolation as Interpolation++import Synthesizer.Filter.Basic (apply, )+import Synthesizer.Filter.Composition (T(..))++import qualified Synthesizer.Plain.Oscillator as Osci+import qualified Synthesizer.Basic.Wave as Wave+import qualified Synthesizer.Plain.Filter.Recursive.FirstOrder as Filt1+import qualified Synthesizer.Plain.Filter.NonRecursive as FiltNR++import qualified Algebra.Module as Module+import qualified Algebra.Transcendental as Trans+import qualified Algebra.RealField as RealField+import qualified Algebra.Field as Field+import qualified Algebra.Absolute as Absolute++import Data.Maybe (fromMaybe)++import NumericPrelude.Base+import NumericPrelude.Numeric++++{-* Reconstruction of the sound of a plucked guitar string -}++guitarInit :: Field.C a => [a]+guitarInit = map (/128) (+ 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 :+ 1 : 2 : 2 : 2 : 2 : 2 : 2 : 2 :+ 2 : 2 : 2 : 2 : 2 : 2 : 2 : 2 :+ 2 : 2 : 2 : 3 : 3 : 3 : 3 : 3 :+ 3 : 3 : 3 : 3 : 3 : 3 : 3 : 3 :+ 3 : 3 : 3 : 4 : 4 : 4 : 4 : 4 :+ 4 : 4 : 4 : 4 : 4 : 4 : 4 : 4 :+ 5 : 5 : 5 : 5 : 5 : 5 : 5 : 5 :+ 6 : 6 : 6 : 7 : 7 : 8 : 8 : 9 :+ 10 : 11 : 12 : 13 : 14 : 15 : 15 : 16 :+ 17 : 17 : 17 : 18 : 18 : 18 : 18 : 18 :+ 18 : 18 : 18 : 17 : 17 : 16 : 16 : 15 :+ 15 : 14 : 14 : 14 : 13 : 13 : 14 : 14 :+ 15 : 16 : 17 : 18 : 19 : 20 : 22 : 23 :+ 25 : 27 : 30 : 32 : 35 : 37 : 39 : 41 :+ 43 : 45 : 47 : 48 : 49 : 49 : 48 : 46 :+ 41 : 34 : 24 : 11 : -6 : -26 : -48 : -72 :+ -96 : -114 : -128 : -128 : -128 : -128 : -128 : -128 :+ -128 : -125 : -110 : -93 : -75 : -57 : -41 : -27 :+ -17 : -10 : -6 : -4 : -2 : -2 : -2 : -2 :+ -2 : -3 : -4 : -4 : -5 : -6 : -7 : -8 :+ -9 : -10 : -11 : -12 : -12 : -12 : -13 : -13 :+ -13 : -13 : -13 : -13 : -12 : -12 : -11 : -10 :+ -9 : -9 : -8 : -8 : -7 : -6 : -6 : -5 :+ -5 : -5 : -5 : -4 : -4 : -4 : -4 : -4 :+ -4 : -4 : -4 : -4 : -4 : -5 : -7 : -8 :+ -8 : -9 : -10 : -11 : -12 : -13 : -13 : -14 :+ -14 : -14 : -13 : -10 : -7 : -2 : 5 : 15 :+ 26 : 37 : 49 : 61 : 73 : 83 : 92 : 99 :+ 105 : 109 : 111 : 112 : 110 : 105 : 99 : 90 :+ 80 : 71 : 63 : 57 : 52 : 49 : 47 : 47 :+ 48 : 49 : 51 : 51 : 52 : 52 : 50 : 48 :+ 42 : 34 : 22 : 7 : -12 : -32 : -56 : -78 :+ -96 : -114 : -127 : -128 : -128 : -128 : -128 : -128 :+ -128 : -118 : -102 : -83 : -67 : -50 : -37 : -26 :+ -17 : -12 : -8 : -5 : -3 : -3 : -2 : -2 :+ -2 : -3 : -4 : -4 : -6 : -7 : -8 : -10 :+ -11 : -12 : -12 : -13 : [])++guitarCompShort, guitarCompLong ::+ Field.C a => [a] -> Composition.T TwoWay.T Double a a+guitarCompShort past = Feedback (Prim (TwoWay.Past past)) (Parallel [+ Serial [Prim (TwoWay.Delay 1),+ Prim (TwoWay.Mask [0.6519177892575342, 0.2331904728998289])],+ Serial [Prim (TwoWay.Delay 126),+ Prim (TwoWay.Mask [0.08253506238277844,+ 0.2369601607320473, 0.18367848836060044,+ -0.06422525077173147, -0.31836517142623727])]])+guitarCompLong past = Feedback (Prim (TwoWay.Past past)) (+ Serial [Prim (TwoWay.Delay 122),+ Prim (TwoWay.Mask [+ -0.23742303494466988,+ 0.020278040917954415,+ 0.12495333789385828,+ 0.16125537461091102,+ 0.1993410924766678,+ 0.24673057006071691,+ 0.25438881375430467,+ 0.1424676847770117,+ 0.03848071949084291,+ -0.016618282409355676,+ -0.04517323927531556,+ -0.0061713683480988475,+ 0.11137126130878339+ ])])++{-| Reconstruct the guitar sound from the sampled initial wave+ and the analysed feedback factors.+ This sounds pretty like the sampled sound. -}+guitarRaw :: (Field.C a, Module.C a a) => [a]+guitarRaw =+ let gi = guitarInit -- assert monomorphism+ y = TwoWay.future+ (TwoWay.delay (length gi)+ (apply (guitarCompLong (reverse gi))+ (TwoWay.Signal [] [])))+ in y++{-| Reconstruct the guitar sound from the sampled initial wave+ but with simple smoothing on feedback.+ This sounds more statically. -}+guitarRawSimple :: (Field.C a, Module.C a a) => [a]+guitarRawSimple =+ let gi = guitarInit -- assert monomorphism+ y = gi ++ drop (length gi)+ (FiltNR.delay 128 (Filt1.lowpass+ (repeat (Filt1.Parameter (0.4 `asTypeOf` head y))) y))+ in y++{-| Reconstruct the guitar sound with the analysed feedback factors+ but with an synthetic initial wave.+ The sharpness of the initial wave can be controlled.+ This is used to implement various velocities. -}+guitarRawVelo :: (Absolute.C a, Trans.C a, Module.C a a) => a -> [a]+guitarRawVelo velo =+ let len = 128::Int+ wave =+ map (Wave.power01Normed velo)+ (take len (iterate (+ 2 / fromIntegral len) (-1)))+ y = TwoWay.future+ (TwoWay.delay len+ (apply (guitarCompLong wave)+ (TwoWay.Signal [] [])))+ in y+++{-| Resample the reconstructed string sound+ so that notes can be played. -}+guitar :: (RealField.C a, Module.C a a) => a -> [a]+guitar freq =+ let srcFreq = 128 * freq+ in Interpolation.multiRelativeZeroPadLinear 0+ (repeat (srcFreq `asTypeOf` freq)) guitarRawSimple++++{-* Tests for FilterGraphs -}++type CompositionDouble =+ Composition.T TwoWay.T Double Double Double++{-| a simple lowpass used to create an exponential2 -}+--expo :: (RealField.C a, Module.C a a) => TwoWay.Signal a+expo :: TwoWay.Signal Double+expo =+ let _flt1 = Feedback (Serial [Prim (OneWay.Delay ([0] `asTypeOf` past))])+ (Serial [Prim (OneWay.Mask+ ([0.9] `asTypeOf` past))])+ _flt2 = (Prim (TwoWay.Mask ([0.5] `asTypeOf` past)))+ :: CompositionDouble+ flt3 = (Feedback (Serial [])+ (Prim (TwoWay.Delay 1)))+ :: CompositionDouble+ TwoWay.Signal past future = apply flt3 (TwoWay.Signal [] [1])+ in TwoWay.Signal past (take 10 future)++type GraphDouble f = Graph.T f Int Double Double Double++simpleGraph :: TwoWay.Signal Double+simpleGraph =+ let out =+ Graph.apply+ (Graph.fromList+ [(0, []),+ (1, [(0, TwoWay.Delay (-1))]),+ (2, [(1, TwoWay.Mask [0.95])])] ::+ GraphDouble TwoWay.T)+ (Graph.signalFromList+ [(0, TwoWay.Signal [] [1])])+ in fromMaybe (error "requested output of non-existing socket")+ (Graph.lookupSignal out (2::Int))++expoGraphTwoWay :: [Double]+expoGraphTwoWay =+ let out =+ Graph.apply+ (Graph.fromList+ [(0, [(2, TwoWay.Past [1])]),+ (1, [(0, TwoWay.Delay 1)]),+ (2, [(1, TwoWay.Mask [0.95])])] ::+ GraphDouble TwoWay.T)+ (Graph.signalFromList+ [(0, TwoWay.Signal [] [])])+ in TwoWay.take 20 $ TwoWay.delay 10+ (fromMaybe (error "requested output of non-existing socket")+ (Graph.lookupSignal out (0::Int)))+++expoGraph :: [Double]+expoGraph =+ let out =+ Graph.apply+ (Graph.fromList+ [(0, [(1, OneWay.Delay [0])]),+ (1, [(0, OneWay.Mask [0.99])])] ::+ GraphDouble OneWay.T)+ (Graph.signalFromList+ [(0, [1])])+ in fromMaybe (error "requested output of non-existing socket")+ (Graph.lookupSignal out (0::Int))++{-| make recursive flanger with help of the two way interpolation -}+flangedSaw :: Double -> [Double]+flangedSaw sampleRate =+ let {- The flanger's principal filter frequency will vary between+ flangeFreq * 2**flangeRange and flangeFreq / 2**flangeRange -}+ flangeFreq = 1000+ flangeRange = 2+ sawFreq = 440+ gain = 0.6+ vol = 0.5++ {- 'control' contains the feedback times -}+ control = map (\c -> sampleRate/flangeFreq * 2**(-flangeRange*c))+ (map sin (iterate (pi/(0.5*sampleRate)+) 0))+ sawPast = Osci.freqModSaw 0 (repeat (-sawFreq/sampleRate))+ sawFuture = Osci.freqModSaw 0 (repeat ( sawFreq/sampleRate))+ --lowNoise = amplify vol noise+ flt = Feedback+ (Prim (TwoWay.Mask [vol]))+ (Serial [Prim (TwoWay.Mask [gain]),+ Prim (TwoWay.Past []),+ Prim (TwoWay.ModFracDelay+ Interpolation.linear+ (TwoWay.Signal [] control))])+ :: CompositionDouble++ in TwoWay.future+ (apply flt (TwoWay.Signal sawPast sawFuture))
+ src/Synthesizer/Filter/Fix.hs view
@@ -0,0 +1,38 @@+module Synthesizer.Filter.Fix where++import qualified Synthesizer.Filter.Graph as Graph+++{-|+A 'Graph.T' with numbered nodes is not very comfortable.+Better provide a 'Control.Monad.Fix.fix'-like function+which allows to enter a graph this way:++> fix $ \[v,w,y] ->+> [a·(u + d·w),+> b·(v + e·y),+> c· w]++-}++type T filter t a v =+ [Channel filter t a v] -> [[(Channel filter t a v, filter t a v)]]++type ChannelId = Int++data Channel filter t a v =+ Channel {channelId :: ChannelId,+ channelInputs :: [(ChannelId, filter t a v)]}+++fix :: T filter t a v -> [Channel filter t a v]+fix f =+ let cs = zipWith (\n inputs ->+ Channel n (map (\(c,filt) -> (channelId c, filt)) inputs))+ [0 ..] (f cs)+ in cs+++toGraph :: T filter t a v -> Graph.T filter Int t a v+toGraph =+ Graph.fromList . map (\(Channel n inputs) -> (n, inputs)) . fix
+ src/Synthesizer/Filter/Graph.hs view
@@ -0,0 +1,183 @@+{-# LANGUAGE NoImplicitPrelude #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE UndecidableInstances #-}+{-# LANGUAGE FlexibleContexts #-}+module Synthesizer.Filter.Graph where++import qualified Prelude as P+import NumericPrelude.Base+import NumericPrelude.Numeric++import qualified Synthesizer.Filter.Basic as FilterBasic+import Synthesizer.Filter.Basic (Filter, apply, )+import qualified Data.Map as Map+import Data.Map(Map)+import MathObj.DiscreteMap() {- Module.C instances for Map -}++import qualified Number.Complex as Complex+import qualified Algebra.RealRing as RealRing+import qualified Algebra.Additive as Additive+import qualified Algebra.Transcendental as Trans+import qualified Algebra.Module as Module+import Algebra.Module((*>))+import Orthogonals(Scalar,inverse,add_to_diagonal)+++{-|+A filter network is a graph consisting+of nodes (input and output signals)+and edges (filter processes).+Output signals can be taken from every node,+inputs can be injected in some nodes+which means that the signal at this node is superposed with+the injected signal.+The same can be achieved by duplicating the network,+one duplicate per input,+and superposing the corresponding outputs.+It is also sensible to setup a graph without inputs,+e.g. a recursive filter with some initial conditions+that works independent from any input.++In opposition to electric filter networks+digital filter networks must be directed.++Test-case: leap-frog filters like++> +-----------[d]-----------++> v |+>(u) -+-> [a] (v) -+-> [b] (w) -+-> [c] (y) -+->+> ^ |+> +-----------[e]-----------+++@+v = a·(u + d·w)+w = b·(v + e·y)+y = c· w+@++We model the general network by a list of nodes,+where each node is an adder that holds a list of its inputs.+Each input of a node is an output+of another node that has gone through a processor.+Additionally there may be one input from outside.+In principle a processor could be a simple filter network+as defined by the structure 'Filter'.++The network is an applyable filter+whenever each circle contains a delay.+To compute the transfer function+we have to solve a system of linear equations+which we can construct quite straight forward+from the processors' input lists.++The current design can be abstractly seen+as the system of linear equations:++ y = A*y + u++where A is a matrix containing the edges hosting the filters,+y the vector of output signals,+u the vector of input signals.+In this formulation the number of inputs and outputs must match+but since you are free to ignore some of the inputs and outputs+you can use nodes for pure output, pure input or both of them.++-}++newtype T filter i t a v =+ C (Map i+ [(i, {- index of the processor whose output goes in here -}+ filter t a v {- description of the filter -}+ )])+++newtype Signal list i v = Signal (Map i (list v))+++fromList :: (Ord i) => [(i, [(i, filter t a v)])] -> T filter i t a v+fromList = C . Map.fromList++toList :: T filter i t a v -> [(i, [(i, filter t a v)])]+toList (C fg) = Map.toList fg++signalFromList :: (Ord i) => [(i, list v)] -> Signal list i v+signalFromList = Signal . Map.fromList++signalToList :: Signal list i v -> [(i, list v)]+signalToList (Signal x) = Map.toList x++lookupSignal :: (Ord i) => Signal list i v -> i -> Maybe (list v)+lookupSignal (Signal x) = flip Map.lookup x+++{-+ These instance may help to include FilterGraphs+ in even bigger structures.+-}+instance (Ord i, Additive.C (list v), Eq (list v))+ => Additive.C (Signal list i v) where+ zero = Signal Additive.zero+ (+) (Signal x) (Signal y) = Signal ((Additive.+) x y)+ (-) (Signal x) (Signal y) = Signal ((Additive.-) x y)+ negate (Signal x) = Signal (Additive.negate x)++instance (Ord i, Eq a, Additive.C a, Additive.C (list v), Eq (list v),+ Module.C a v, Module.C a (list v))+ => Module.C a (Signal list i v) where+ s *> (Signal x) = Signal (s *> x)+++{-+ It would be interesting to make FilterGraphs+ an instance of Filter.+ To achieve that we had to make GraphSignals an instance of Module.C+ and the transferFunction would no longer return a factor+ but a function that maps input amplitudes+ of a given frequency to output amplitudes.++instance (Ord i, Show i, Filter list filter) =>+ Filter (Signal list i) (T filter i) where+-}++apply :: (Ord i, Show i, Additive.C t, Trans.C t, RealRing.C t,+ Module.C a v, Module.C a (list v),+ Filter list filter) =>+ T filter i t a v -> Signal list i v -> Signal list i v+apply (C fg) (Signal inputs) =+ let getInput i = Map.findWithDefault Additive.zero i inputs+ getOutput i = Map.findWithDefault+ (error ("Unknown processor: "++show i)) i outputs+ output i edges =+ foldl (Additive.+) (getInput i) (map (\(j,f) ->+ FilterBasic.apply f (getOutput j)) edges)+ outputs = Map.mapWithKey output fg+ in Signal outputs++{-| Compute a matrix that tells how an input frequency+ is mapped to the various output nodes.++ According to the formulation given above+ we have to invert the matrix (I-A).++ Currently this is done by a QR decomposition for each frequency.+ It would be probably faster if we decompose+ the matrix containing polynomial elements.+ Then the inverted matrix would consist of some+ polynomial ratios which can be evaluated for each frequency.+-}+transferFunction ::+ (Ord i, Show i, Trans.C t,+ P.Fractional (Complex.T t), Scalar (Complex.T t),+ Module.C a t, Filter list filter) =>+ T filter i t a v -> t -> [[Complex.T t]]+transferFunction (C fg) w =+ let keys = Map.keys fg+ elts = Map.elems fg+ inputsToMap procs =+ Map.mapWithKey (\_ f -> FilterBasic.transferFunction f w)+ (Map.fromList procs)+ makeRow procs =+ map (flip (Map.findWithDefault 0) (inputsToMap procs)) keys+ matrix = map makeRow elts+ in inverse (add_to_diagonal (-1) matrix)
+ src/Synthesizer/Filter/Graphic.hs view
@@ -0,0 +1,7 @@+module Synthesizer.Filter.Graphic where++{-|+ This module should be populated with functions+ that create flowchart graphics from the filter networks+ of the 'Composition' module.+-}
+ src/Synthesizer/Filter/MonadFix.hs view
@@ -0,0 +1,44 @@+module Synthesizer.Filter.MonadFix where++import qualified Synthesizer.Filter.Graph as Graph+import qualified Synthesizer.Filter.Fix as FFix++import Synthesizer.Filter.Fix (Channel(Channel), ChannelId)++import Control.Monad.Trans.State (StateT, evalStateT, get, modify, )+import Control.Monad.Trans.Writer (Writer, execWriter, tell, )+import Control.Monad.Trans.Class (lift, )+++{-|+If you find 'Filter.Fix.T' still inconvenient,+and if you don't care about portability,+you can also use the following monad with the @mdo@ notation.++> mdo+> v <- a·(u + d·w)+> w <- b·(v + e·y)+> y <- c· w++-}+++type T filter t a v x = StateT ChannelId (Writer [Channel filter t a v]) x++makeChannel ::+ [(ChannelId, filter t a v)] ->+ T filter t a v ChannelId+makeChannel inputs =+ do n <- get+ modify succ+ lift $ tell [Channel n inputs]+ return n+++run :: T filter t a v x -> [Channel filter t a v]+run m = execWriter (evalStateT m 0)+++toGraph :: T filter t a v x -> Graph.T filter Int t a v+toGraph =+ Graph.fromList . map (\(Channel n inputs) -> (n, inputs)) . run
+ src/Synthesizer/Filter/OneWay.hs view
@@ -0,0 +1,76 @@+{-# LANGUAGE NoImplicitPrelude #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleInstances #-}+module Synthesizer.Filter.OneWay where++import Synthesizer.Filter.Basic++import qualified Synthesizer.Plain.Interpolation as Interpolation+import qualified Synthesizer.Plain.Filter.NonRecursive as FiltNR+import Number.Complex(cis)++import qualified Algebra.Module as Module+import qualified Algebra.Ring as Ring+import qualified Algebra.Additive as Additive++import Algebra.Module(linearComb)+import Algebra.Additive(zero)++import NumericPrelude.Base+import NumericPrelude.Numeric++type Signal = []++{-| shift signal in time -}+delay :: (Additive.C v) =>+ Int -> Signal v -> Signal v+delay = FiltNR.delayPad zero++delayOnce :: (Additive.C v) =>+ Signal v -> Signal v+delayOnce = (zero:)+++{-| Unmodulated non-recursive filter -}+nonRecursiveFilter :: Module.C a v =>+ [a] -> [v] -> [v]+nonRecursiveFilter = FiltNR.generic++{-| Modulated non-recursive filter. -}+nonRecursiveFilterMod :: Module.C a v =>+ [[a]] -> [v] -> [v]+nonRecursiveFilterMod ms x =+ zipWith linearComb ms (tail (scanl (flip (:)) [] x))+++{-| Description of a basic filter that can be used in larger networks. -}+data T t a v =+ Mask [a]+ {-^ A static filter described by its mask -}+ | ModMask (Signal [a])+ {-^ A modulated filter described by a list of masks -}+ | FracDelay (Interpolation.T t v) t+ {-^ Delay the signal by a fractional amount of samples.+ This is achieved by interpolation. -}+ | ModFracDelay (Interpolation.T t v) (Signal t)+ {-^ Delay with varying delay times.+ The delay times sequence must monotonically decrease.+ (This includes constant parts!) -}+ | Delay [v]+ {-^ Delay the signal by prepending another one -}++instance Filter [] T where++ apply (Mask m) = nonRecursiveFilter m+ apply (ModMask m) = nonRecursiveFilterMod m+ apply (FracDelay ip t) = Interpolation.multiRelativeZeroPad zero+ ip (-t) (repeat 1)+ apply (ModFracDelay ip ts) = Interpolation.multiRelativeZeroPad zero+ ip (- head ts) (repeat 1 - FiltNR.differentiate ts)+ apply (Delay x) = (x++)++ transferFunction (Mask m) w = linearComb m (screw (negate w))+ transferFunction (FracDelay _ t) w = cis (negate w * t)+ transferFunction (Delay x) w = cis (negate w * fromIntegral (length x))+ transferFunction _ _ =+ error "transfer function can't be computed for modulated filters"
+ src/Synthesizer/Filter/TwoWay.hs view
@@ -0,0 +1,247 @@+{-# LANGUAGE NoImplicitPrelude #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleInstances #-}+module Synthesizer.Filter.TwoWay where++import Synthesizer.Filter.Basic++import qualified Synthesizer.Plain.Signal as Sig+import qualified Synthesizer.Plain.Interpolation as Ip+import qualified Synthesizer.Plain.Interpolation as Interpolation++import Algebra.Module(linearComb,(*>))++import qualified Algebra.Module as Module+import qualified Algebra.RealRing as RealRing+import qualified Algebra.Ring as Ring+import qualified Algebra.Additive as Additive++import Number.Complex(cis, )+import Data.Function.HT (nest, )+import qualified Data.List as List++import NumericPrelude.Base hiding (take)+import NumericPrelude.Numeric+++{-| A TwoWay.Signal stores values of the past and the future -}+data Signal v = Signal {past, future :: [v]}+ deriving (Show, Eq)++{-| Take n values starting from time zero.+ If you want clips from elsewhere,+ call 'take' after 'delay'. -}+take :: Int -> Signal v -> [v]+take n (Signal _ x) = List.take n x++zipSignalWith :: (a -> b -> c) -> Signal a -> Signal b -> Signal c+zipSignalWith f (Signal xPast xFuture) (Signal yPast yFuture) =+ (Signal (zipWith f xPast yPast) (zipWith f xFuture yFuture))++{-| Take the value at time zero. -}+origin :: Ring.C a => Signal a -> a+origin (Signal _ (x:_)) = x+origin _ = 0++{-| A signal that consists entirely of ones -}+ones :: Ring.C a => Signal a+ones = Signal (repeat 1) (repeat 1)++{-| shift signal in time,+ keep all values but if required pad with zeros -}+delay :: (Additive.C v) =>+ Int -> Signal v -> Signal v+delay = delayGen delayOnce++delayPad :: v -> Int -> Signal v -> Signal v+delayPad z = delayGen (delayPadOnce z)++{-| shift signal in time,+ zero values at either ends will be flushed -}+delayOpt :: (Eq v, Additive.C v) =>+ Int -> Signal v -> Signal v+delayOpt = delayGen delayOptOnce+++{-| Delay by one sample. -}+delayOnce :: (Additive.C v) =>+ Signal v -> Signal v+--delayOnce (Signal [] []) = ([],[])+delayOnce (Signal [] ys) = Signal [] (zero:ys)+delayOnce (Signal (x:xs) ys) = Signal xs (x:ys)++delayPadOnce :: v -> Signal v -> Signal v+--delayPadOnce _ (Signal [] []) = ([],[])+delayPadOnce z (Signal [] ys) = Signal [] (z:ys)+delayPadOnce _ (Signal (x:xs) ys) = Signal xs (x:ys)++delayOptOnce :: (Eq v, Additive.C v) =>+ Signal v -> Signal v+--delayOptOnce (Signal [] []) = Signal [] []+delayOptOnce (Signal [] ys) = Signal [] (zero:ys)+delayOptOnce (Signal (x:xs) []) = Signal xs (if x==zero then [] else x:[])+delayOptOnce (Signal (x:xs) ys) = Signal xs (x:ys)+++{-| General routine that supports delaying and prefetching+ using a general one-sample delaying routine. -}+delayGen :: (Signal v -> Signal v) ->+ Int -> Signal v -> Signal v+{- Using this optimization applications of recursive filters+ with zero initial conditions represented by an empty list will fail.+ This is because in this case the value of the first item of the future list+ depends on the first item of the input future list,+ whereas normally the first future value depends on no input future value,+ at all.+delayGen _ _ (Signal [] []) = Signal [] []+ cf. the next example -}+delayGen delOnce t =+ if t < 0+ then reverseTwoWay . nest (negate t) delOnce . reverseTwoWay+ else nest t delOnce++reverseTwoWay :: Signal v -> Signal v+reverseTwoWay (Signal x y) = Signal y x+++instance (Additive.C v) => Additive.C (Signal v) where+ zero = Signal zero zero+ (+) (Signal y0 y1) (Signal x0 x1) = Signal (y0 + x0) (y1 + x1)+ (-) (Signal y0 y1) (Signal x0 x1) = Signal (y0 - x0) (y1 - x1)+ negate (Signal x0 x1) = Signal (negate x0) (negate x1)++instance (Module.C a v) => Module.C a (Signal v) where+ (*>) s (Signal x0 x1) = Signal (s *> x0) (s *> x1)+++++{-| for a Signal this means a reversion of the elements -}+flipPair :: (a,b) -> (b,a)+flipPair (x,y) = (y,x)++{- This example simulates what happens if you call+ apply (Feedback (Serial []) (Prim (Delay 1)) []) ([],[1])+ depending on the implementation of delayGen it may work or+ loop infinitely when yFuture is computed.+ It's even before the first element of yFuture is computed.+ Note, that the equivalent+ apply (Feedback (Serial []) (Prim (Delay 1)) [0]) ([],[1])+ works! (i.e. set yPast = [0] -}+testDelayGen :: Signal Double+testDelayGen =+ let yPast = []+ x = Signal [] [1]+ y = Signal yPast yFuture+ Signal _ yFuture = delayOnce (x + y)+ -- Signal _ yFuture = delayOptOnce (add x y)+ -- Signal _ yFuture = delayGen delayOnce 1 (add x y)+ in Signal yPast (List.take 10 yFuture)++++{-| Unmodulated non-recursive filter -}+nonRecursiveFilter :: Module.C a v =>+ [a] -> Signal v -> Signal v+nonRecursiveFilter m x =+ linearComb m (iterate delayOnce x)++{-| Modulated non-recursive filter.+ The number of values before time 0 (past) or+ the filter mask lengths must be at most finite. -}+nonRecursiveFilterMod :: Module.C a v =>+ Signal [a] -> Signal v -> Signal v+nonRecursiveFilterMod (Signal mpre msuf) x =+ let (pre, suf) = unzip (map (\(Signal a b) -> (a,b)) (iterate delayOnce x))+ in Signal (zipWith linearComb mpre pre) (zipWith linearComb msuf suf)+++{-| Interpolation allowing negative frequencies,+ but requires storage of all past values. -}+interpolatePaddedZero :: (Ord a, RealRing.C a) =>+ b -> Interpolation.T a b+ -> a -> Signal a -> Signal b -> Signal b+interpolatePaddedZero z ip phase fs (Signal xPast xFuture) =+ let (phInt, phFrac) = splitFraction phase+ xPadded = Signal (xPast ++ repeat z) (xFuture ++ repeat z)+ in interpolateCore ip phFrac fs+ (delayPad z (Ip.offset ip - phInt) xPadded)++interpolatePaddedCyclic :: (Ord a, RealRing.C a) =>+ Interpolation.T a b+ -> a -> Signal a -> Signal b -> Signal b+interpolatePaddedCyclic ip phase fs (Signal xPast xFuture) =+ let (phInt, phFrac) = splitFraction phase+ xCyclic = xFuture ++ reverse xPast+ in interpolateCore ip phFrac fs+ -- mod is for efficiency, only+ (delayPad (error "interpolate: infinite signal needs no zero padding")+ (mod (Ip.offset ip - phInt) (length xCyclic))+ (Signal (cycle (reverse xCyclic)) (cycle xCyclic)))++-- note that the extrapolation may miss some of the first and some of the last points+interpolatePaddedExtrapolation :: (Ord a, RealRing.C a) =>+ Interpolation.T a b+ -> a -> Signal a -> Signal b -> Signal b+interpolatePaddedExtrapolation ip phase fs x =+ interpolateCore ip (phase - fromIntegral (Ip.offset ip)) fs x++interpolateCore :: (Ord a, Ring.C a) =>+ Interpolation.T a b -> a -> Signal a -> Signal b -> Signal b+interpolateCore ip phase (Signal freqPast freqFuture) x =+ Signal (interpolateHalfWay ip (1-phase) freqPast+ (delayPadOnce (error "interpolateCore: infinite signal needs no zero padding")+ (reverseTwoWay x)))+ (interpolateHalfWay ip phase freqFuture x)++interpolateHalfWay :: (Ord a, Ring.C a) =>+ Interpolation.T a b -> a -> [a] -> Signal b -> [b]+interpolateHalfWay ip phase freqs (Signal xPast xFuture) =+ if phase >= 1 && Sig.lengthAtLeast (1+Ip.number ip) xFuture+ then interpolateHalfWay ip (phase-1) freqs+ (Signal (head xFuture : xPast) (tail xFuture))+ else if phase < 0 && Sig.lengthAtLeast 1 xPast+ then interpolateHalfWay ip (phase + 1) freqs+ (Signal (tail xPast) (head xPast : xFuture))+ else Ip.func ip phase xFuture :+ interpolateHalfWay ip (phase + head freqs) (tail freqs)+ (Signal xPast xFuture)+++{-| Description of a basic filter that can be used in larger networks. -}+data T t a v =+ Mask [a]+ {-^ A static filter described by its mask -}+ | ModMask (Signal [a])+ {-^ A modulated filter described by a list of masks -}+ | FracDelay (Interpolation.T t v) t+ {-^ Delay the signal by a fractional amount of samples.+ This is achieved by interpolation. -}+ | ModFracDelay (Interpolation.T t v) (Signal t)+ {-^ Delay with varying delay times. -}+ | Delay Int+ {-^ Delay the signal by given amount of samples. -}+ | Past [v]+ {-^ Replace the past by the given one.+ This must be present in each recursive filter cycle+ to let the magic work! -}++instance Filter Signal T where++ apply (Mask m) = nonRecursiveFilter m+ apply (ModMask m) = nonRecursiveFilterMod m+ apply (FracDelay ip t) = interpolatePaddedZero zero+ ip (-t) ones+ apply (ModFracDelay ip ts) = interpolatePaddedZero zero+ ip (- origin ts) (ts - delay (-1) ts + ones)+ apply (Delay t) = delay t+ apply (Past x) = Signal x . future++ {- This is in principle the same as for one way filters.+ How can one merge them? -}+ transferFunction (Mask m) w = linearComb m (screw (negate w))+ transferFunction (FracDelay _ t) w = cis (negate w * t)+ transferFunction (Delay t) w = cis (negate w * fromIntegral t)+ transferFunction (Past _) _ = 1+ transferFunction _ _ =+ error "transfer function can't be computed for modulated filters"
+ synthesizer-filter.cabal view
@@ -0,0 +1,49 @@+Name: synthesizer-filter+Version: 0.4+License: GPL+License-File: LICENSE+Author: Henning Thielemann <haskell@henning-thielemann.de>+Maintainer: Henning Thielemann <haskell@henning-thielemann.de>+Homepage: http://www.haskell.org/haskellwiki/Synthesizer+Category: Sound+Synopsis: Audio signal processing coded in Haskell: Filter networks+Description:+ In this package we experiment with various ways+ of representing filter networks.+ However, none of them is mature so far.+Stability: Experimental+Tested-With: GHC==6.8.2, GHC==6.10.4+Cabal-Version: >=1.6+Build-Type: Simple++Source-Repository this+ Tag: 0.4+ Type: darcs+ Location: http://code.haskell.org/synthesizer/filter/++Source-Repository head+ Type: darcs+ Location: http://code.haskell.org/synthesizer/filter/++Library+ Build-Depends:+ synthesizer-core >=0.4 && <0.5,+ transformers >=0.2 && <0.3,+ numeric-prelude >=0.2 && <0.3,+ numeric-quest >= 0.1 && <0.2,+ utility-ht >=0.0.5 && <0.1,+ containers >=0.1 && <0.4,+ base >= 3 && <5++ GHC-Options: -Wall+ Hs-source-dirs: src+ Exposed-modules:+ Synthesizer.Filter.Basic+ Synthesizer.Filter.Composition+ Synthesizer.Filter.Example+ Synthesizer.Filter.Fix+ Synthesizer.Filter.Graph+ Synthesizer.Filter.Graphic+ Synthesizer.Filter.MonadFix+ Synthesizer.Filter.OneWay+ Synthesizer.Filter.TwoWay