[Haskell-cafe] How to implement a digital filter, using Arrows?

[Captain Freako]

Hi John,
Thanks for this reply:

> Date: Tue, 18 Oct 2011 14:05:22 +1030
> From: John Lask <jvlask at hotmail.com>
> Subject: Re: [Haskell-cafe] How to implement a digital filter, using
>        Arrows?
> To: haskell-cafe at haskell.org
> Message-ID: <BLU0-
> SMTP384394452FD2750FBE3BCFCC6E50 at phx.gbl>
> Content-Type: text/plain; charset="ISO-8859-1"; format=flowed
>
>
>
> your function corresponds with Control.Arrow.Transformer.Automaton. If
> you frame your function is such most of your plumbing is taken care of.
>
Following your advice, I arrived at:

  1 {-# LANGUAGE Arrows, GeneralizedNewtypeDeriving, FlexibleContexts #-}
  2
  3 module Filter (
  4     FilterState
  5   , Filter
  6   , applyFilter
  7   , convT
  8 ) where
  9
 10 import EitherT
 11 import Control.Monad
 12 import Control.Monad.State
 13 import Control.Arrow
 14 import Control.Arrow.Operations
 15 import Control.Arrow.Transformer
 16 import Control.Arrow.Transformer.All
 17 import Data.Stream as DS (fromList, toList)
 18
 19 -- tap weights, `as' and `bs', are being made part of the filter state,
in
 20 -- order to accomodate adaptive filters (i.e. - DFEs).
 21 data FilterState a = FilterState {
 22     as   :: [a] -- transfer function denominator coefficients
 23   , bs   :: [a] -- transfer function numerator coefficients
 24   , taps :: [a] -- current delay tap stored values
 25   }
 26
 27 -- Future proofing the implementation, using the `newtype' trick.
 28 newtype Filter b c = F {
 29     runFilter :: (b, FilterState b) -> (c, FilterState b)
 31   }
 32
 33 -- Time domain convolution filter (FIR or IIR),
 34 -- expressed in direct form 2
 35 convT :: (Num b) => Filter b b
 36 convT = F $ \(x, s) ->
 37     let wk = (x - sum [a * t | (a, t) <- zip (tail $ as s) (taps s)])
 38         newTaps = wk : ((reverse . tail . reverse) $ taps s)
 39         s' = s {taps = newTaps}
 40         y  = sum [b * w | (b, w) <- zip (bs s) (wk : (taps s))]
 41     in (y, s')
 42
 43 -- Turn a filter into an Automaton, in order to use the built in
plubming
 44 -- of Arrows to run the filter on an input.
 45 filterAuto :: (ArrowApply a) => Filter b c -> FilterState b -> Automaton
a (e, b) c
 46 filterAuto f s = Automaton a where
 47     a = proc (e, x) -> do
 48         (y, s') <- arr (runFilter f) -< (x, s)
 49         returnA -< (y, filterAuto f s')
 50
 53 applyFilter :: Filter b c -> FilterState b -> [b] -> ([c], FilterState
b)
 54 applyFilter f s =
 55     let a = filterAuto f s
 56     in proc xs -> do
 57         ys <- runAutomaton a -< ((), DS.fromList xs)
 58         s' <- (|fetch|)
 59         returnA -< (DS.toList ys, s')
 60

which gave me this compile error:

> Filter.hs:58:16:
>     Could not deduce (ArrowState (FilterState b) (->))
>       from the context ()
>       arising from a use of `fetch' at Filter.hs:58:16-20
>     Possible fix:
>       add (ArrowState (FilterState b) (->)) to the context of
>         the type signature for `applyFilter'
>       or add an instance declaration for
>          (ArrowState (FilterState b) (->))
>     In the expression: fetch
>     In the expression:
>         proc xs -> do { ys <- runAutomaton a -< ((), fromList xs);
>                         s' <- (|fetch |);
>                         returnA -< (toList ys, s') }
>     In the expression:
>         let a = filterAuto f s
>         in
>           proc xs -> do { ys <- runAutomaton a -< ((), fromList xs);
>                           s' <- (|fetch |);
>                           .... }
>
So, I made this change:

 51 applyFilter :: *(ArrowState (FilterState b) (->)) =>* Filter b c ->
FilterState b -> [b] ->
 52                                                     ([c], FilterState b)

And that compiled. However, when I tried to test my new filter with:

> let s = FilterState [1,0,0] [0.7, 0.2, 0.1] [0, 0, 0]
> applyFilter convT s [1,0,0,0,0]

I got:

> <interactive>:1:0:
>     No instance for (ArrowState (FilterState Double) (->))
>       arising from a use of `applyFilter' at <interactive>:1:0-30
>     Possible fix:
>       add an instance declaration for
>       (ArrowState (FilterState Double) (->))
>     In the expression: applyFilter convT s [1, 0, 0, 0, ....]
>     In the definition of `it': it = applyFilter convT s [1, 0, 0, ....]
>
I thought, "maybe, I need to derive from *ArrowState* in my *Filter* type
definition."
So, I tried making this change to the code:

28 newtype Filter b c = F {
29     runFilter :: (b, FilterState b) -> (c, FilterState b)
30   } deriving (ArrowState (FilterState x))

but then I was back to no compile:

> Filter.hs:30:14:
>     Can't make a derived instance of
>       `ArrowState (FilterState x) Filter'
>       (even with cunning newtype deriving):
>       cannot eta-reduce the representation type enough
>     In the newtype declaration for `Filter'
>
Do you have any advice?

Thanks,
-db
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