module Synthesizer.Dimensional.Cyclic.Analysis (
toFrequencySpectrum, fromFrequencySpectrum,
) where
import qualified Synthesizer.Generic.Cut as CutG
import qualified Synthesizer.State.Analysis as Ana
import qualified Synthesizer.State.Signal as Sig
import qualified Synthesizer.Dimensional.Rate as Rate
import qualified Synthesizer.Dimensional.Amplitude as Amp
import qualified Synthesizer.Dimensional.Signal.Private as SigA
import qualified Synthesizer.Dimensional.Cyclic.Signal as SigC
import qualified Number.DimensionTerm as DN
import qualified Algebra.DimensionTerm as Dim
import Number.DimensionTerm ((&*&), (*&), )
import qualified Number.Complex as Complex
import qualified Algebra.Transcendental as Trans
import qualified Algebra.Field as Field
import NumericPrelude.Base ((.), )
import NumericPrelude.Numeric ((+), negate, (/), fromIntegral, pi, )
import Prelude (Int, )
period :: (Field.C t, Dim.C u, CutG.Read body) =>
SigA.T (Rate.Dimensional u t) amp (SigC.T body) ->
DN.T u t
period = makePhysicalPeriod (fromIntegral . CutG.length)
makePhysicalPeriod :: (Field.C t, Dim.C u) =>
(body -> t) ->
SigA.T (Rate.Dimensional u t) amp (SigC.T body) ->
DN.T u t
makePhysicalPeriod f x =
f (SigC.toPeriod (SigA.body x))
*& DN.unrecip (SigA.actualSampleRate x)
toFrequencySpectrum :: (Trans.C q, Dim.C u, Dim.C v) =>
SigA.T (Rate.Dimensional u q) (Amp.Dimensional v q) (SigC.T (Sig.T (Complex.T q))) ->
SigA.T (Rate.Dimensional (Dim.Recip u) q) (Amp.Dimensional (Dim.Mul u v) q) (SigC.T (Sig.T (Complex.T q)))
toFrequencySpectrum x =
let len = DN.rewriteDimension Dim.doubleRecip (period x)
amp = SigA.actualAmplitude x
ss = SigC.toPeriod (SigA.body x)
n = Sig.length ss
z = Complex.cis (negate (pi+pi) / fromIntegral n)
newAmp = DN.unrecip (SigA.actualSampleRate x) &*& amp
in SigA.Cons
(Rate.Actual len)
(Amp.Numeric newAmp)
(SigC.Cons (Sig.take n (Ana.chirpTransform z ss)))
fromFrequencySpectrum :: (Trans.C q, Dim.C u, Dim.C v) =>
SigA.T (Rate.Dimensional (Dim.Recip u) q) (Amp.Dimensional (Dim.Mul u v) q) (SigC.T (Sig.T (Complex.T q))) ->
SigA.T (Rate.Dimensional u q) (Amp.Dimensional v q) (SigC.T (Sig.T (Complex.T q)))
fromFrequencySpectrum x =
let len = period x
amp = SigA.actualAmplitude x
ss = SigC.toPeriod (SigA.body x)
n = Sig.length ss
z = Complex.cis ((pi+pi) / fromIntegral n)
newAmp =
DN.rewriteDimension
(Dim.identityLeft . Dim.applyLeftMul Dim.cancelLeft . Dim.associateLeft)
(DN.unrecip (SigA.actualSampleRate x) &*& amp)
in SigA.Cons
(Rate.Actual len)
(Amp.Numeric newAmp)
(SigC.Cons (Sig.take n (Ana.chirpTransform z ss)))