Synthesizer.Plain.Filter.Recursive.SecondOrder

All recursive filters with real coefficients can be decomposed into first order and second order filters with real coefficients. This follows from the Fundamental theorem of algebra.

Documentation

data Parameter a

Parameters for a general recursive filter of 2nd order.

Constructors

Parameter

Fields

• c0, c1, c2, d1, d2 :: !a

Instances

Functor Parameter

Methods

fmap :: (a -> b) -> Parameter a -> Parameter b

(<$) :: a -> Parameter b -> Parameter a

Applicative Parameter

Methods

pure :: a -> Parameter a

(<*>) :: Parameter (a -> b) -> Parameter a -> Parameter b

(*>) :: Parameter a -> Parameter b -> Parameter b

(<*) :: Parameter a -> Parameter b -> Parameter a

Foldable Parameter

Methods

fold :: Monoid m => Parameter m -> m

foldMap :: Monoid m => (a -> m) -> Parameter a -> m

foldr :: (a -> b -> b) -> b -> Parameter a -> b

foldr' :: (a -> b -> b) -> b -> Parameter a -> b

foldl :: (b -> a -> b) -> b -> Parameter a -> b

foldl' :: (b -> a -> b) -> b -> Parameter a -> b

foldr1 :: (a -> a -> a) -> Parameter a -> a

foldl1 :: (a -> a -> a) -> Parameter a -> a

toList :: Parameter a -> [a]

null :: Parameter a -> Bool

length :: Parameter a -> Int

elem :: Eq a => a -> Parameter a -> Bool

maximum :: Ord a => Parameter a -> a

minimum :: Ord a => Parameter a -> a

sum :: Num a => Parameter a -> a

product :: Num a => Parameter a -> a

Traversable Parameter

Methods

traverse :: Applicative f => (a -> f b) -> Parameter a -> f (Parameter b)

sequenceA :: Applicative f => Parameter (f a) -> f (Parameter a)

mapM :: Monad m => (a -> m b) -> Parameter a -> m (Parameter b)

sequence :: Monad m => Parameter (m a) -> m (Parameter a)

C a v => C a (Parameter v)

Methods

scaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v)

Show a => Show (Parameter a)

Methods

showsPrec :: Int -> Parameter a -> ShowS

show :: Parameter a -> String

showList :: [Parameter a] -> ShowS

Storable a => Storable (Parameter a)

Methods

sizeOf :: Parameter a -> Int

alignment :: Parameter a -> Int

peekElemOff :: Ptr (Parameter a) -> Int -> IO (Parameter a)

pokeElemOff :: Ptr (Parameter a) -> Int -> Parameter a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Parameter a)

pokeByteOff :: Ptr b -> Int -> Parameter a -> IO ()

peek :: Ptr (Parameter a) -> IO (Parameter a)

poke :: Ptr (Parameter a) -> Parameter a -> IO ()

data State a

Constructors

State

Fields

• u1, u2, y1, y2 :: !a

Instances

Functor State

Methods

fmap :: (a -> b) -> State a -> State b

(<$) :: a -> State b -> State a

Applicative State

Methods

pure :: a -> State a

(<*>) :: State (a -> b) -> State a -> State b

(*>) :: State a -> State b -> State b

(<*) :: State a -> State b -> State a

Foldable State

Methods

fold :: Monoid m => State m -> m

foldMap :: Monoid m => (a -> m) -> State a -> m

foldr :: (a -> b -> b) -> b -> State a -> b

foldr' :: (a -> b -> b) -> b -> State a -> b

foldl :: (b -> a -> b) -> b -> State a -> b

foldl' :: (b -> a -> b) -> b -> State a -> b

foldr1 :: (a -> a -> a) -> State a -> a

foldl1 :: (a -> a -> a) -> State a -> a

toList :: State a -> [a]

null :: State a -> Bool

length :: State a -> Int

elem :: Eq a => a -> State a -> Bool

maximum :: Ord a => State a -> a

minimum :: Ord a => State a -> a

sum :: Num a => State a -> a

product :: Num a => State a -> a

Traversable State

Methods

traverse :: Applicative f => (a -> f b) -> State a -> f (State b)

sequenceA :: Applicative f => State (f a) -> f (State a)

mapM :: Monad m => (a -> m b) -> State a -> m (State b)

sequence :: Monad m => State (m a) -> m (State a)

Show a => Show (State a)

Methods

showsPrec :: Int -> State a -> ShowS

show :: State a -> String

showList :: [State a] -> ShowS

Storable a => Storable (State a)

Methods

sizeOf :: State a -> Int

alignment :: State a -> Int

peekElemOff :: Ptr (State a) -> Int -> IO (State a)

pokeElemOff :: Ptr (State a) -> Int -> State a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (State a)

pokeByteOff :: Ptr b -> Int -> State a -> IO ()

peek :: Ptr (State a) -> IO (State a)

poke :: Ptr (State a) -> State a -> IO ()

adjustPassband :: C a => Passband -> (a -> Parameter a) -> a -> Parameter a

Given a function which computes the filter parameters of a lowpass filter for a given frequency, turn that into a function which generates highpass parameters, if requested filter type is Highpass.

amplify :: C a => a -> Parameter a -> Parameter a

Change filter parameter such that result is amplified by a given factor.

causal :: (C a, C a v) => T (Parameter a, v) v

modifier :: (C a, C a v) => Simple (State v) (Parameter a) v v

modifierInit :: (C a, C a v) => Initialized (State v) (State v) (Parameter a) v v

run :: (C a, C a v) => T (Parameter a) -> T v -> T v

runInit :: (C a, C a v) => State v -> T (Parameter a) -> T v -> T v

step :: (C a, C a v) => Parameter a -> v -> State (State v) v

zeroState :: C a => State a