Numeric.EMD

Empirical Mode Decomposition (Hilbert-Huang Transform) in pure Haskell.

Main interface is emd, with defaultEO. A tracing version that outputs a log to stdout is also available, as emdTrace. This can be used to help track down a specific IMF that might be taking more time than desired.

EMD (Hilbert-Huang Transform)

emd :: (Vector v a, KnownNat n, Fractional a, Ord a) => EMDOpts a -> Vector v (n + 2) a -> EMD v (n + 2) a

EMD decomposition (Hilbert-Huang Transform) of a given time series with a given sifting stop condition.

emdTrace :: (Vector v a, KnownNat n, Fractional a, Ord a, MonadIO m) => EMDOpts a -> Vector v (n + 2) a -> m (EMD v (n + 2) a)

emd, but tracing results to stdout as IMFs are found. Useful for debugging to see how long each step is taking.

emd' :: (Vector v a, KnownNat n, Fractional a, Ord a, Applicative m) => (SiftResult v (n + 2) a -> m r) -> EMDOpts a -> Vector v (n + 2) a -> m (EMD v (n + 2) a)

emd with a callback for each found IMF.

data EMD v n a

An EMD v n a is a Hilbert-Huang transform of a time series with n items of type a stored in a vector v.

Constructors

EMD

Fields

• emdIMFs :: ![Vector v n a]
• emdResidual :: !(Vector v n a)

Instances

Show (v a) => Show (EMD v n a)

Defined in Numeric.EMD

Methods

showsPrec :: Int -> EMD v n a -> ShowS

show :: EMD v n a -> String

showList :: [EMD v n a] -> ShowS

data EMDOpts a

Options for EMD composition.

Constructors

EO

Fields

• eoSiftCondition :: SiftCondition a

  stop condition for sifting

• eoSplineEnd :: SplineEnd

  end conditions for envelope splines

• eoClampEnvelope :: Bool

  if True, use time series endpoints as part of min and max envelopes

Instances

Eq a => Eq (EMDOpts a)

Defined in Numeric.EMD

Methods

(==) :: EMDOpts a -> EMDOpts a -> Bool

(/=) :: EMDOpts a -> EMDOpts a -> Bool

Ord a => Ord (EMDOpts a)

Defined in Numeric.EMD

Methods

compare :: EMDOpts a -> EMDOpts a -> Ordering

(<) :: EMDOpts a -> EMDOpts a -> Bool

(<=) :: EMDOpts a -> EMDOpts a -> Bool

(>) :: EMDOpts a -> EMDOpts a -> Bool

(>=) :: EMDOpts a -> EMDOpts a -> Bool

max :: EMDOpts a -> EMDOpts a -> EMDOpts a

min :: EMDOpts a -> EMDOpts a -> EMDOpts a

Show a => Show (EMDOpts a)

Defined in Numeric.EMD

Methods

showsPrec :: Int -> EMDOpts a -> ShowS

show :: EMDOpts a -> String

showList :: [EMDOpts a] -> ShowS

defaultEO :: Fractional a => EMDOpts a

Default EMDOpts

data SiftCondition a

Stop conditions for sifting process

Constructors

SCStdDev a

Stop using standard SD method

SCTimes Int

Stop after a fixed number of iterations

SCOr (SiftCondition a) (SiftCondition a)

one or the other

SCAnd (SiftCondition a) (SiftCondition a)

both conditions met

Instances

Eq a => Eq (SiftCondition a)

Defined in Numeric.EMD

Methods

(==) :: SiftCondition a -> SiftCondition a -> Bool

(/=) :: SiftCondition a -> SiftCondition a -> Bool

Ord a => Ord (SiftCondition a)

Defined in Numeric.EMD

Methods

compare :: SiftCondition a -> SiftCondition a -> Ordering

(<) :: SiftCondition a -> SiftCondition a -> Bool

(<=) :: SiftCondition a -> SiftCondition a -> Bool

(>) :: SiftCondition a -> SiftCondition a -> Bool

(>=) :: SiftCondition a -> SiftCondition a -> Bool

max :: SiftCondition a -> SiftCondition a -> SiftCondition a

min :: SiftCondition a -> SiftCondition a -> SiftCondition a

Show a => Show (SiftCondition a)

Defined in Numeric.EMD

Methods

showsPrec :: Int -> SiftCondition a -> ShowS

show :: SiftCondition a -> String

showList :: [SiftCondition a] -> ShowS

defaultSC :: Fractional a => SiftCondition a

Default SiftCondition

data SplineEnd

End condition for spline

Constructors

SENotAKnot

SENatural

Instances

Eq SplineEnd

Defined in Numeric.EMD.Internal.Spline

Methods

(==) :: SplineEnd -> SplineEnd -> Bool

(/=) :: SplineEnd -> SplineEnd -> Bool

Ord SplineEnd

Defined in Numeric.EMD.Internal.Spline

Methods

compare :: SplineEnd -> SplineEnd -> Ordering

(<) :: SplineEnd -> SplineEnd -> Bool

(<=) :: SplineEnd -> SplineEnd -> Bool

(>) :: SplineEnd -> SplineEnd -> Bool

(>=) :: SplineEnd -> SplineEnd -> Bool

max :: SplineEnd -> SplineEnd -> SplineEnd

min :: SplineEnd -> SplineEnd -> SplineEnd

Show SplineEnd

Defined in Numeric.EMD.Internal.Spline

Methods

showsPrec :: Int -> SplineEnd -> ShowS

show :: SplineEnd -> String

showList :: [SplineEnd] -> ShowS

Internal

sift :: (Vector v a, KnownNat n, Fractional a, Ord a) => EMDOpts a -> Vector v (n + 2) a -> SiftResult v (n + 2) a

Iterated sifting process, used to produce either an IMF or a residual.

data SiftResult v n a

The result of a sifting operation. Each sift either yields a residual, or a new IMF.

Constructors

SRResidual !(Vector v n a)

SRIMF !(Vector v n a) !Int

envelopes :: (Vector v a, KnownNat n, Fractional a, Ord a) => SplineEnd -> Bool -> Vector v (n + 2) a -> Maybe (Vector v (n + 2) a, Vector v (n + 2) a)

Returns cubic splines of local minimums and maximums. Returns Nothing if there are not enough local minimum or maximums to create the splines.