synthesizer-core-0.8.2.1: Audio signal processing coded in Haskell: Low level part

Copyright (c) Henning Thielemann 2008-2012 GPL synthesizer@henning-thielemann.de provisional requires multi-parameter type classes None Haskell2010

Synthesizer.Plain.Filter.Recursive.Universal

Description

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

Synopsis

# Documentation

data Parameter a Source #

Constructors

 Parameter Fieldsk1, k2, ampIn, ampI1, ampI2, ampLimit :: !a
Instances
 Source # Instance details Methodsfmap :: (a -> b) -> Parameter a -> Parameter b #(<) :: a -> Parameter b -> Parameter a # Source # Instance details Methodspure :: a -> Parameter a #(<*>) :: Parameter (a -> b) -> Parameter a -> Parameter b #liftA2 :: (a -> b -> c) -> Parameter a -> Parameter b -> Parameter c #(*>) :: Parameter a -> Parameter b -> Parameter b #(<*) :: Parameter a -> Parameter b -> Parameter a # Source # Instance details Methodsfold :: 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 # Source # Instance details Methodstraverse :: 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) Source # Instance details MethodsscaleAndAccumulate :: (a, Parameter v) -> (Parameter v, Parameter v -> Parameter v) Source # Storable a => Storable (Parameter a) Source # Instance details MethodssizeOf :: 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 Source # Constructors  Result Fieldshighpass, bandpass, lowpass, bandlimit :: !a Instances  Source # Instance details Methodsfmap :: (a -> b) -> Result a -> Result b #(<) :: a -> Result b -> Result a # Source # Instance details Methodspure :: a -> Result a #(<*>) :: Result (a -> b) -> Result a -> Result b #liftA2 :: (a -> b -> c) -> Result a -> Result b -> Result c #(*>) :: Result a -> Result b -> Result b #(<*) :: Result a -> Result b -> Result a # Source # Instance details Methodsfold :: 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 # Source # Instance details Methodstraverse :: 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) Source # Instance details Methods(*>) :: a -> Result v -> Result v # Storable a => Storable (Result a) Source # Instance details MethodssizeOf :: 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) Source # Instance details Methodszero :: Result v #(+) :: Result v -> Result v -> Result v #(-) :: Result v -> Result v -> Result v #negate :: Result v -> Result v #

type State v = (v, v) Source #

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

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

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

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

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.

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) Source #

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

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

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

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

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 Source #

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.