úÎ!Š2„a      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`None.SUVX_uaemd>Treats every item in a "plateu" as a local minimum or maximum.aNone .HUVXkƒbemd :https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm Will return c8 if the matrix is not invertible. This will happen if: +The first item in the main diagonal is zeroœThere is any i such that b_{i + 1} = a_i * c_i. That is, an item in the main diagonal is equal to the product of the off-diagonal elements a row above itAnother mystery condition!bemda: Bottom diagonal of Memdb: Main diagonal of Memdc: Upper diagonal of Memdyemdx such that M x = yb(c) Justin Le 2018BSD3 justin@jle.im experimental non-portableNone "#&'.07UVXk emd1D Cubic splinedemdaeemdbfemdy_{i-1}gemdy_ihemd x_i - x_{i-1}emdEnd condition for splineemdc"Not-a-knot" condition: third derivatives are continuous at endpoints. Default for matlab spline.emd@"Natural" condition: curve becomes a straight line at endpoints.emdH"Clamped" condition: Slope of curves at endpoints are explicitly given.emd!Sample a spline at a given point.emdaBuild a cubic spline based on control points using given end conditions (not-a-knot, or natural) 2https://en.wikipedia.org/wiki/Spline_interpolationemdemd(x, y)iemdderivative at left endemdderivative at right end(c) Justin Le 2018BSD3 justin@jle.im experimental non-portableNone"#&'-.7HUVX_k:N emdVThe result of a sifting operation. Each sift either yields a residual, or a new IMF.emdnumber of sifting iterationsemdAn  v n a; is an Empirical Mode Decomposition of a time series with n items of type a stored in a vector v.The component-wise sum of  and 0 should yield exactly the original series (see &).emd#Stop conditions for sifting process<Data type is lazy in its fields, so this infinite data type: nTimes n = SCTimes n  nTimes (n + 1) will be treated identically as: nTimes = SCTimes emdStop using standard SD methodemd/Stop after a fixed number of sifting iterationsemdOne or the otheremd!Stop when both conditions are metemd4Clamp envelope at end points (Matlab implementation)emdExtend boundaries symmetricallyemdOptions for EMD composition.emdstop condition for siftingemd#end conditions for envelope splines emdprocess for handling boundary!emdDefault "emdDefault jemdk if stop#emdNEMD decomposition of a given time series with a given sifting stop condition.$Takes a sized vector to ensure that: The resulting D contains IMFs that are all the same length as the input vector,We provide a vector of size of at least one.$emd#n, but tracing results to stdout as IMFs are found. Useful for debugging to see how long each step is taking.%emd#$ with a callback for each found IMF.&emd Collapse an C back into its original time series. Should be a left-inverse to #: using & on the result of #' should give back the original vector.'emdFIterated sifting process, used to produce either an IMF or a residual.lemd Single sift(emd@Returns cubic splines of local minimums and maximums. Returns cJ if there are not enough local minimum or maximums to create the splines.memd7Build a splined vector against a map of control points.)emd*emd+emd,emd-emd.emd/emdmemd extensions   !"#$%&'( #$%& !"' ((c) Justin Le 2018BSD3 justin@jle.im experimental non-portableNone "#.7>UVXk‚Ô@emdA Hilbert-Huang Transform. An @ 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 G or H.Cemd?A Hilbert Trasnform of a given IMF, given as a "skeleton line".Eemd"IMF HHT Magnitude as a time seriesFemdBIMF HHT instantaneous frequency as a time series (between 0 and 1)GemdfDirectly compute the Hilbert-Huang transform of a given time series. Essentially is a composition of H and #. See H for a more flexible version.HemdOCompute the Hilbert-Huang transform from a given Empirical Mode Decomposition.IemdÅCompute 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.aTakes a "binning" function to allow you to specify how specific you want your frequencies to be.See hhtSparseSpetrum for a sparser version, and K for a denser version.JemdA sparser vesion of IB. Compute the full Hilbert-Huang Transform spectrum. Returns a sparse7 matrix representing the power at each time step (the n n) and frequency (the k).aTakes a "binning" function to allow you to specify how specific you want your frequencies to be.KemdA denser version of I§. Compute the full Hilbert-Huang Transform spectrum, returning a dense matrix (as a vector of vectors) representing the power at each time step and each frequency.;Takes a "binning" function that maps a frequency to one of m7 discrete slots, for accumulation in the dense matrix.Lemd¾Compute the marginal spectrum given a Hilbert-Huang Transform. It is similar to a Fourier Transform; it provides the "total power" over the entire time series for each frequency component.eA binning function is accepted to allow you to specify how specific you want your frequencies to be.MemdšReturns the "expected value" of frequency at each time step, calculated as a weighted average of all contributions at every frequency at that time step.NemdbReturns the dominant frequency (frequency with largest magnitude contribution) at each time step.OemdcCompute the instantaneous energy of the time series at every step via the Hilbert-Huang Transform.Pemd3Degree of stationarity, as a function of frequency.Qemd1Given a time series, return a time series of the  magnitude# of the hilbert transform and the  frequencyo 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.RemdThe polar form of SQ: returns the magnitude and phase of the discrete hilbert transform of a series.ÿFThe computation of magnitude is unique, but computing phase gives us some ambiguity. The interpretation of the hilbert transform for instantaneous frequency is that the original series "spirals" around the complex plane as time progresses, like a helix. So, we impose a constraint on the phase to uniquely determine it:  \phi_{t+1} is the minimal valid phase such that \phi_{t+1} \geq \phi_{t}d. This enforces the phase to be monotonically increasing at the slowest possible detectable rate.`Note that this function effectively resets the initial phase to be zero, conceptually rotating S to begin on the real axis.Semd§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.ŒNumerically assumes that the signal is zero everywhere outside of the vector, instead of the periodic assumption taken by matlab's version.Temd«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, S.ŒNumerically assumes that the signal is zero everywhere outside of the vector, instead of the periodic assumption taken by matlab's version.UemdVemdWemdXemdIemd7binning function. takes rev/tick freq between 0 and 1.Jemd7binning function. takes rev/tick freq between 0 and 1.Kemd7binning function. takes rev/tick freq between 0 and 1.Lemd7binning function. takes rev/tick freq between 0 and 1.Pemd7binning function. takes rev/tick freq between 0 and 1.( !"@ABCDEFGHIJKLMNOPQRST(@ABCDEFHGIJKLOPMN !"STRQo      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEEFGGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxemd-0.1.6.0-inplaceNumeric.EMD.Internal.Spline Numeric.EMD Numeric.HHTNumeric.EMD.Internal.Extrema Numeric.EMD.Internal.TridiagonalSpline SplineEnd SENotAKnot SENatural SEClamped sampleSpline makeSpline$fBinarySplineEnd$fShowSplineEnd $fEqSplineEnd$fOrdSplineEnd$fGenericSplineEnd$fShowSplineCoef SiftResult SRResidualSRIMFEMDemdIMFs emdResidual SiftConditionSCStdDevSCTimesSCOrSCAndBoundaryHandlerBHClamp BHSymmetricEMDOptsEOeoSiftCondition eoSplineEndeoBoundaryHandler defaultEO defaultSCemdemdTraceemd'iemdsift envelopes$fBinaryBoundaryHandler$fDefaultSiftCondition$fBinarySiftCondition$fDefaultEMDOpts$fBinaryEMDOpts $fBinaryEMD $fNFDataEMD$fShowBoundaryHandler$fEqBoundaryHandler$fOrdBoundaryHandler$fGenericBoundaryHandler$fShowSiftCondition$fEqSiftCondition$fOrdSiftCondition$fGenericSiftCondition $fShowEMDOpts $fEqEMDOpts $fOrdEMDOpts$fGenericEMDOpts $fShowEMD $fGenericEMD$fEqEMD$fOrdEMDHHThhtLinesHHTLinehlMagshlFreqshhthhtEmd hhtSpectrumhhtSparseSpectrumhhtDenseSpectrummarginal expectedFreq dominantFreqinstantaneousEnergydegreeOfStationarityhilbertMagFreq hilbertPolarhilbert hilbertIm$fNFDataHHTLine$fBinaryHHTLine $fNFDataHHT $fBinaryHHT $fShowHHTLine $fEqHHTLine $fOrdHHTLine$fGenericHHTLine $fShowHHT$fEqHHT$fOrdHHT $fGenericHHTextremasolveTridiagonalbase GHC.MaybeNothing_scAlpha_scBeta _scGamma0 _scGamma1_scDeltaclamped testConditionghc-prim GHC.TypesTruesift' splineAgainstXfinite-typelits-0.1.4.2-7d241a11b2813bf176fcf1f914f3665e4fd52b732c1cda6c1eedd668fda5fc53Data.Finite.InternalFinite