Synthesizer.Plain.Filter.Recursive.FirstOrderComplex

First order lowpass and highpass with complex valued feedback. The complex feedback allows resonance. It is often called complex resonator.

Documentation

data Parameter a

Instances

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

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

The internal parameters are computed such that:

• At the resonance frequency the filter amplifies by the factor resonance with no phase shift.
• At resonance frequency plus half sample rate the filter amplifies by facter recip $ 2 - recip resonance with no phase shift, but you cannot observe this immediately, because it is outside the Nyquist band.

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

The internal parameters are computed such that:

• At the resonance frequency the filter amplifies by the factor resonance with no phase shift.
• At resonance frequency plus and minus band width the filter amplifies by facter 1 with a non-zero phase shift.

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

The internal parameters are computed such that:

• At the resonance frequency the filter amplifies by the factor resonance with a non-zero phase shift.
• The filter amplifies the direct current (frequency zero) by factor 1 with no phase shift.
• The real component is a lowpass, the imaginary component is a highpass. You can interpolate between them using other complex projections.

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

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

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

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

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

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

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