Synthesizer.Plain.Filter.Recursive.Universal

State variable filter. One filter that generates lowpass, bandpass, highpass, bandlimit at once.

Documentation

data Parameter a

Constructors

Parameter

Fields

• k1, k2, ampIn, ampI1, ampI2, ampLimit :: !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)

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 Result a

Constructors

Result

Fields

• highpass, bandpass, lowpass, bandlimit :: !a

Instances

Functor Result

Methods

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

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

Applicative Result

Methods

pure :: a -> Result a

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

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

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

Foldable Result

Methods

fold :: Monoid m => Result m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Result a -> a

foldl1 :: (a -> a -> a) -> Result a -> a

toList :: Result a -> [a]

null :: Result a -> Bool

length :: Result a -> Int

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

maximum :: Ord a => Result a -> a

minimum :: Ord a => Result a -> a

sum :: Num a => Result a -> a

product :: Num a => Result a -> a

Traversable Result

Methods

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

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

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

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

C a v => C a (Result v)

Methods

(*>) :: a -> Result v -> Result v

Storable a => Storable (Result a)

Methods

sizeOf :: Result a -> Int

alignment :: Result a -> Int

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

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

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

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

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

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

C v => C (Result v)

Methods

zero :: Result v

(+) :: Result v -> Result v -> Result v

(-) :: Result v -> Result v -> Result v

negate :: Result v -> Result v

type State v = (v, v)

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

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

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

parameter :: C a => Pole a -> Parameter a

The computation of the internal parameters is a bit complicated, but it fulfills the following properties:

• At the resonance frequency the band pass has 180 degree phase shift. This is also approximately the frequency where the filter has maximum output. Even more important, this is the frequency where the band limit filter works.
• At the resonance frequency highpass, lowpass, and bandpass amplify by the factor resonance.
• The lowpass amplifies the frequency zero by factor 1.
• The highpass amplifies the highest representable (Nyquist) frequency by the factor 1.
• The bandlimit amplifies both frequency zero and Nyquist frequency by factor one and cancels the resonance frequency.

parameterToSecondOrderLowpass :: C a => Parameter a -> Parameter a

Convert parameters of universal filter to general second order filter parameters. Filtering with these parameters does not yield exactly the same result since the initial conditions are different.

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

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

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

Universal filter: Computes high pass, band pass, low pass in one go

parameterAlt :: C a => Pole a -> Parameter a

The computation of the internal parameters is a bit complicated, but it fulfills the following properties:

• At the resonance frequency the band pass has 180 degree phase shift. This is also approximately the frequency where the filter has maximum output. Even more important, this is the frequency where the band limit filter works.
• At the resonance frequency highpass, lowpass, and bandpass amplify by the factor resonance.
• The lowpass amplifies the frequency zero by factor 1.
• The highpass amplifies the highest representable (Nyquist) frequency by the factor 1.
• The bandlimit amplifies both frequency zero and Nyquist frequency by factor one and cancels the resonance frequency.

parameterOld :: C a => Pole a -> Parameter a

The computation of the internal parameters is a bit complicated, but it fulfills the following properties:

• At the resonance frequency the band pass has 180 degree phase shift. This is also approximately the frequency where the filter has maximum output. Even more important, this is the frequency where the band limit filter works.
• At the resonance frequency highpass, lowpass, and bandpass amplify by the factor resonance.
• The lowpass amplifies the frequency zero by factor 1.
• The highpass amplifies the highest representable (Nyquist) frequency by the factor 1.
• The bandlimit amplifies both frequency zero and Nyquist frequency by factor one and cancels the resonance frequency.