module DSP.Correlation (rxy, rxy_b, rxy_u, rxx, rxx_b, rxx_u, test) where
import Data.Array
import Data.Complex
rxy :: (Ix a, Integral a, RealFloat b) => Array a (Complex b)
-> Array a (Complex b)
-> a
-> Complex b
rxy :: forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy Array a (Complex b)
x Array a (Complex b)
y a
k =
if a
k forall a. Ord a => a -> a -> Bool
>= a
0
then forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum [ Array a (Complex b)
xforall i e. Ix i => Array i e -> i -> e
!(a
iforall a. Num a => a -> a -> a
+a
k) forall a. Num a => a -> a -> a
* forall a. Num a => Complex a -> Complex a
conjugate (Array a (Complex b)
yforall i e. Ix i => Array i e -> i -> e
!a
i) | a
i <- [a
0..(a
nforall a. Num a => a -> a -> a
-a
1forall a. Num a => a -> a -> a
-a
k)] ]
else forall a. Num a => Complex a -> Complex a
conjugate (forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy Array a (Complex b)
y Array a (Complex b)
x (-a
k))
where n :: a
n = forall a b. (a, b) -> b
snd (forall i e. Array i e -> (i, i)
bounds Array a (Complex b)
x) forall a. Num a => a -> a -> a
+ a
1
rxy_b :: (Ix a, Integral a, RealFloat b) => Array a (Complex b)
-> Array a (Complex b)
-> a
-> Complex b
rxy_b :: forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy_b Array a (Complex b)
x Array a (Complex b)
y a
k = forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy Array a (Complex b)
x Array a (Complex b)
y a
k forall a. Fractional a => a -> a -> a
/ forall a b. (Integral a, Num b) => a -> b
fromIntegral a
n
where n :: a
n = forall a b. (a, b) -> b
snd (forall i e. Array i e -> (i, i)
bounds Array a (Complex b)
x) forall a. Num a => a -> a -> a
+ a
1
rxy_u :: (Ix a, Integral a, RealFloat b) => Array a (Complex b)
-> Array a (Complex b)
-> a
-> Complex b
rxy_u :: forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy_u Array a (Complex b)
x Array a (Complex b)
y a
k = forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy Array a (Complex b)
x Array a (Complex b)
y a
k forall a. Fractional a => a -> a -> a
/ forall a b. (Integral a, Num b) => a -> b
fromIntegral (a
n forall a. Num a => a -> a -> a
- forall a. Num a => a -> a
abs a
k)
where n :: a
n = forall a b. (a, b) -> b
snd (forall i e. Array i e -> (i, i)
bounds Array a (Complex b)
x) forall a. Num a => a -> a -> a
+ a
1
rxx :: (Ix a, Integral a, RealFloat b) => Array a (Complex b)
-> a
-> Complex b
rxx :: forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> a -> Complex b
rxx Array a (Complex b)
x a
k = forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy Array a (Complex b)
x Array a (Complex b)
x a
k
rxx_b :: (Ix a, Integral a, RealFloat b) => Array a (Complex b)
-> a
-> Complex b
rxx_b :: forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> a -> Complex b
rxx_b Array a (Complex b)
x a
k = forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy_b Array a (Complex b)
x Array a (Complex b)
x a
k
rxx_u :: (Ix a, Integral a, RealFloat b) => Array a (Complex b)
-> a
-> Complex b
rxx_u :: forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> a -> Complex b
rxx_u Array a (Complex b)
x a
k = forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy_u Array a (Complex b)
x Array a (Complex b)
x a
k
xt, yt :: Array Int (Complex Double)
xt :: Array Int (Complex Double)
xt = forall i e. Ix i => (i, i) -> [(i, e)] -> Array i e
array (Int
0,Int
4)
[ (Int
0, Double
1 forall a. a -> a -> Complex a
:+ Double
0),
(Int
1, Double
0 forall a. a -> a -> Complex a
:+ Double
1),
(Int
2, (-Double
1) forall a. a -> a -> Complex a
:+ Double
0),
(Int
3, Double
0 forall a. a -> a -> Complex a
:+ (-Double
1)),
(Int
4, Double
1 forall a. a -> a -> Complex a
:+ Double
0) ]
yt :: Array Int (Complex Double)
yt = forall i e. Ix i => (i, i) -> [(i, e)] -> Array i e
array (Int
0,Int
4)
[ (Int
0, Double
1 forall a. a -> a -> Complex a
:+ Double
0),
(Int
1, (-Double
1) forall a. a -> a -> Complex a
:+ Double
0),
(Int
2, Double
1 forall a. a -> a -> Complex a
:+ Double
0),
(Int
3, (-Double
1) forall a. a -> a -> Complex a
:+ Double
0),
(Int
4, Double
1 forall a. a -> a -> Complex a
:+ Double
0) ]
rt :: [Complex Double]
rt :: [Complex Double]
rt = forall a b. (a -> b) -> [a] -> [b]
map (forall a b.
(Ix a, Integral a, RealFloat b) =>
Array a (Complex b) -> Array a (Complex b) -> a -> Complex b
rxy_b Array Int (Complex Double)
xt Array Int (Complex Double)
yt) [ Int
0, Int
1, Int
2 ]
test :: Bool
test :: Bool
test = [Complex Double]
rt forall a. Eq a => a -> a -> Bool
== [ (Double
0.2 forall a. a -> a -> Complex a
:+ Double
0.0), (Double
0.0 forall a. a -> a -> Complex a
:+ Double
0.0), (Double
0.0 forall a. a -> a -> Complex a
:+ Double
0.2) ]