Numeric.HHT

Hilbert-Huang transform in pure Haskell.

The main data type is HHT, which can be generated using hht or hhtEmd. See Numeric.EMD for information on why this module uses "sized vectors", and how to convert unsized vectors to sized vectors.

Since: emd-0.1.2.0

Documentation

hhtEmd :: forall v n a. (Vector v a, KnownNat n, RealFloat a) => EMD v (n + 1) a -> HHT v n a

Compute the Hilbert-Huang transform from a given Empirical Mode Decomposition.

hht :: forall v n a. (Vector v a, KnownNat n, RealFloat a) => EMDOpts a -> Vector v (n + 1) a -> HHT v n a

Directly compute the Hilbert-Huang transform of a given time series. Essentially is a composition of hhtEmd and emd. See hhtEmd for a more flexible version.

hhtSpectrum

Arguments

:: (KnownNat n, Ord k, Num a)

=> (a -> k)

binning function. takes rev/tick freq between 0 and 1.

-> HHT Vector n a

-> Vector n (Map k a)

Compute the full Hilbert-Huang Transform spectrum. At each timestep is a sparse map of frequency components and their respective magnitudes. Frequencies not in the map are considered to be zero.

Takes a "binning" function to allow you to specify how specific you want your frequencies to be.

marginal

Arguments

:: (Vector v a, KnownNat n, Ord k, Num a)

=> (a -> k)

binning function. takes rev/tick freq between 0 and 1.

-> HHT v n a

-> Map k a

Compute the marginal spectrum given a Hilbert-Huang Transform. A binning function is accepted to allow you to specify how specific you want your frequencies to be.

instantaneousEnergy :: forall v n a. (Vector v a, KnownNat n, Num a) => HHT v n a -> Vector v n a

Compute the instantaneous energy of the time series at every step via the Hilbert-Huang Transform.

degreeOfStationarity

Arguments

:: (Vector v a, KnownNat n, Ord k, Fractional a)

=> (a -> k)

binning function. takes rev/tick freq between 0 and 1.

-> HHT v n a

-> Map k a

Degree of stationarity, as a function of frequency.

newtype HHT v n a

A Hilbert-Huang Transform. An HHT v n a is a Hilbert-Huang transform of an n-item time series of items of type a represented using vector v.

Create using hht or hhtEmd.

Constructors

HHT

Fields

• hhtLines :: [HHTLine v n a]

Instances

Eq (v a) => Eq (HHT v n a)

Defined in Numeric.HHT

Methods

(==) :: HHT v n a -> HHT v n a -> Bool

(/=) :: HHT v n a -> HHT v n a -> Bool

Ord (v a) => Ord (HHT v n a)

Defined in Numeric.HHT

Methods

compare :: HHT v n a -> HHT v n a -> Ordering

(<) :: HHT v n a -> HHT v n a -> Bool

(<=) :: HHT v n a -> HHT v n a -> Bool

(>) :: HHT v n a -> HHT v n a -> Bool

(>=) :: HHT v n a -> HHT v n a -> Bool

max :: HHT v n a -> HHT v n a -> HHT v n a

min :: HHT v n a -> HHT v n a -> HHT v n a

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

Defined in Numeric.HHT

Methods

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

show :: HHT v n a -> String

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

Generic (HHT v n a)

Defined in Numeric.HHT

Associated Types

type Rep (HHT v n a) :: * -> *

Methods

from :: HHT v n a -> Rep (HHT v n a) x

to :: Rep (HHT v n a) x -> HHT v n a

(Vector v a, KnownNat n, Binary (v a)) => Binary (HHT v n a)

Defined in Numeric.HHT

Methods

put :: HHT v n a -> Put

get :: Get (HHT v n a)

putList :: [HHT v n a] -> Put

type Rep (HHT v n a)

Defined in Numeric.HHT

type Rep (HHT v n a) = D1 (MetaData "HHT" "Numeric.HHT" "emd-0.1.3.0-8B9GLcXbOZ06FyHsmMMhXM" True) (C1 (MetaCons "HHT" PrefixI True) (S1 (MetaSel (Just "hhtLines") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [HHTLine v n a])))

data HHTLine v n a

A Hilbert Trasnform of a given IMF, given as a "skeleton line".

Constructors

HHTLine

Fields

• hlMags :: !(Vector v n a)

  IMF HHT Magnitude as a time series

• hlFreqs :: !(Vector v n a)

  IMF HHT instantaneous frequency as a time series (between 0 and 1)

Instances

Eq (v a) => Eq (HHTLine v n a)

Defined in Numeric.HHT

Methods

(==) :: HHTLine v n a -> HHTLine v n a -> Bool

(/=) :: HHTLine v n a -> HHTLine v n a -> Bool

Ord (v a) => Ord (HHTLine v n a)

Defined in Numeric.HHT

Methods

compare :: HHTLine v n a -> HHTLine v n a -> Ordering

(<) :: HHTLine v n a -> HHTLine v n a -> Bool

(<=) :: HHTLine v n a -> HHTLine v n a -> Bool

(>) :: HHTLine v n a -> HHTLine v n a -> Bool

(>=) :: HHTLine v n a -> HHTLine v n a -> Bool

max :: HHTLine v n a -> HHTLine v n a -> HHTLine v n a

min :: HHTLine v n a -> HHTLine v n a -> HHTLine v n a

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

Defined in Numeric.HHT

Methods

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

show :: HHTLine v n a -> String

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

Generic (HHTLine v n a)

Defined in Numeric.HHT

Associated Types

type Rep (HHTLine v n a) :: * -> *

Methods

from :: HHTLine v n a -> Rep (HHTLine v n a) x

to :: Rep (HHTLine v n a) x -> HHTLine v n a

(Vector v a, KnownNat n, Binary (v a)) => Binary (HHTLine v n a)

Defined in Numeric.HHT

Methods

put :: HHTLine v n a -> Put

get :: Get (HHTLine v n a)

putList :: [HHTLine v n a] -> Put

type Rep (HHTLine v n a)

Defined in Numeric.HHT

type Rep (HHTLine v n a) = D1 (MetaData "HHTLine" "Numeric.HHT" "emd-0.1.3.0-8B9GLcXbOZ06FyHsmMMhXM" False) (C1 (MetaCons "HHTLine" PrefixI True) (S1 (MetaSel (Just "hlMags") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Vector v n a)) :*: S1 (MetaSel (Just "hlFreqs") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Vector v n a))))

data EMDOpts a

Options for EMD composition.

Constructors

EO

Fields

• eoSiftCondition :: SiftCondition a

  stop condition for sifting

• eoSplineEnd :: SplineEnd a

  end conditions for envelope splines

• eoBoundaryHandler :: Maybe BoundaryHandler

  process for handling boundary

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

Generic (EMDOpts a)

Defined in Numeric.EMD

Associated Types

type Rep (EMDOpts a) :: * -> *

Methods

from :: EMDOpts a -> Rep (EMDOpts a) x

to :: Rep (EMDOpts a) x -> EMDOpts a

Binary a => Binary (EMDOpts a)

Defined in Numeric.EMD

Methods

put :: EMDOpts a -> Put

get :: Get (EMDOpts a)

putList :: [EMDOpts a] -> Put

Fractional a => Default (EMDOpts a)

Defined in Numeric.EMD

Methods

def :: EMDOpts a

type Rep (EMDOpts a)

Defined in Numeric.EMD

type Rep (EMDOpts a) = D1 (MetaData "EMDOpts" "Numeric.EMD" "emd-0.1.3.0-8B9GLcXbOZ06FyHsmMMhXM" False) (C1 (MetaCons "EO" PrefixI True) (S1 (MetaSel (Just "eoSiftCondition") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (SiftCondition a)) :*: (S1 (MetaSel (Just "eoSplineEnd") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (SplineEnd a)) :*: S1 (MetaSel (Just "eoBoundaryHandler") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe BoundaryHandler)))))

defaultEO :: Fractional a => EMDOpts a

Default EMDOpts

data BoundaryHandler

Constructors

BHClamp

Clamp envelope at end points (Matlab implementation)

BHSymmetric

Extend boundaries symmetrically

Instances

Eq BoundaryHandler

Defined in Numeric.EMD

Methods

(==) :: BoundaryHandler -> BoundaryHandler -> Bool

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

Ord BoundaryHandler

Defined in Numeric.EMD

Methods

compare :: BoundaryHandler -> BoundaryHandler -> Ordering

(<) :: BoundaryHandler -> BoundaryHandler -> Bool

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

(>) :: BoundaryHandler -> BoundaryHandler -> Bool

(>=) :: BoundaryHandler -> BoundaryHandler -> Bool

max :: BoundaryHandler -> BoundaryHandler -> BoundaryHandler

min :: BoundaryHandler -> BoundaryHandler -> BoundaryHandler

Show BoundaryHandler

Defined in Numeric.EMD

Methods

showsPrec :: Int -> BoundaryHandler -> ShowS

show :: BoundaryHandler -> String

showList :: [BoundaryHandler] -> ShowS

Generic BoundaryHandler

Defined in Numeric.EMD

Associated Types

type Rep BoundaryHandler :: * -> *

Methods

from :: BoundaryHandler -> Rep BoundaryHandler x

to :: Rep BoundaryHandler x -> BoundaryHandler

Binary BoundaryHandler

Defined in Numeric.EMD

Methods

put :: BoundaryHandler -> Put

get :: Get BoundaryHandler

putList :: [BoundaryHandler] -> Put

type Rep BoundaryHandler

Defined in Numeric.EMD

type Rep BoundaryHandler = D1 (MetaData "BoundaryHandler" "Numeric.EMD" "emd-0.1.3.0-8B9GLcXbOZ06FyHsmMMhXM" False) (C1 (MetaCons "BHClamp" PrefixI False) (U1 :: * -> *) :+: C1 (MetaCons "BHSymmetric" PrefixI False) (U1 :: * -> *))

data SiftCondition a

Stop conditions for sifting process

Data type is lazy in its fields, so this infinite data type:

nTimes n = SCTimes n SCOr nTimes (n + 1)

will be treated identically as:

nTimes = SCTimes

Constructors

SCStdDev !a

Stop using standard SD method

SCTimes !Int

Stop after a fixed number of sifting iterations

SCOr (SiftCondition a) (SiftCondition a)

One or the other

SCAnd (SiftCondition a) (SiftCondition a)

Stop when both conditions are 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

Generic (SiftCondition a)

Defined in Numeric.EMD

Associated Types

type Rep (SiftCondition a) :: * -> *

Methods

from :: SiftCondition a -> Rep (SiftCondition a) x

to :: Rep (SiftCondition a) x -> SiftCondition a

Binary a => Binary (SiftCondition a)

Defined in Numeric.EMD

Methods

put :: SiftCondition a -> Put

get :: Get (SiftCondition a)

putList :: [SiftCondition a] -> Put

Fractional a => Default (SiftCondition a)

Defined in Numeric.EMD

Methods

def :: SiftCondition a

type Rep (SiftCondition a)

Defined in Numeric.EMD

type Rep (SiftCondition a) = D1 (MetaData "SiftCondition" "Numeric.EMD" "emd-0.1.3.0-8B9GLcXbOZ06FyHsmMMhXM" False) ((C1 (MetaCons "SCStdDev" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) :+: C1 (MetaCons "SCTimes" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int))) :+: (C1 (MetaCons "SCOr" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (SiftCondition a)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (SiftCondition a))) :+: C1 (MetaCons "SCAnd" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (SiftCondition a)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (SiftCondition a)))))

defaultSC :: Fractional a => SiftCondition a

Default SiftCondition

data SplineEnd a

End condition for spline

Constructors

SENotAKnot

"Not-a-knot" condition: third derivatives are continuous at endpoints. Default for matlab spline.

SENatural

"Natural" condition: curve becomes a straight line at endpoints.

SEClamped a a

"Clamped" condition: Slope of curves at endpoints are explicitly given.

Since: emd-0.1.2.0

Instances

Eq a => Eq (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Methods

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

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

Ord a => Ord (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Methods

compare :: SplineEnd a -> SplineEnd a -> Ordering

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

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

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

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

max :: SplineEnd a -> SplineEnd a -> SplineEnd a

min :: SplineEnd a -> SplineEnd a -> SplineEnd a

Show a => Show (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Methods

showsPrec :: Int -> SplineEnd a -> ShowS

show :: SplineEnd a -> String

showList :: [SplineEnd a] -> ShowS

Generic (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Associated Types

type Rep (SplineEnd a) :: * -> *

Methods

from :: SplineEnd a -> Rep (SplineEnd a) x

to :: Rep (SplineEnd a) x -> SplineEnd a

Binary a => Binary (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

Methods

put :: SplineEnd a -> Put

get :: Get (SplineEnd a)

putList :: [SplineEnd a] -> Put

type Rep (SplineEnd a)

Defined in Numeric.EMD.Internal.Spline

type Rep (SplineEnd a) = D1 (MetaData "SplineEnd" "Numeric.EMD.Internal.Spline" "emd-0.1.3.0-8B9GLcXbOZ06FyHsmMMhXM" False) (C1 (MetaCons "SENotAKnot" PrefixI False) (U1 :: * -> *) :+: (C1 (MetaCons "SENatural" PrefixI False) (U1 :: * -> *) :+: C1 (MetaCons "SEClamped" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))))

Hilbert transforms (internal usage)

hilbert :: forall v n a. (Vector v a, Vector v (Complex a), KnownNat n, Floating a) => Vector v n a -> Vector v n (Complex a)

Real part is original series and imaginary part is hilbert transformed series. Creates a "helical" form of the original series that rotates along the complex plane.

Numerically assumes that the signal is zero everywhere outside of the vector, instead of the periodic assumption taken by matlab's version.

hilbertIm :: forall v n a. (Vector v a, KnownNat n, Floating a) => Vector v n a -> Vector v n a

Hilbert transformed series. Essentially the same series, but phase-shifted 90 degrees. Is so-named because it is the "imaginary part" of the proper hilbert transform, hilbert.

Numerically assumes that the signal is zero everywhere outside of the vector, instead of the periodic assumption taken by matlab's version.

hilbertMagFreq :: forall v n a. (Vector v a, KnownNat n, RealFloat a) => Vector v (n + 1) a -> (Vector v (n + 1) a, Vector v n a)

Given a time series, return a time series of the magnitude of the hilbert transform and the frequency of the hilbert transform, in units of revolutions per tick. Is only expected to taken in proper/legal IMFs.

The frequency will always be between 0 and 1, since we can't determine anything faster given the discretization, and we exclude negative values as physically unmeaningful for an IMF.