TS_HANTS

The TS_HANTS (Harmonic ANalysis of Time Series) function can be used to smooth noisy data or interpolate data to reconstruct incomplete images. This is accomplished by calculating a Fourier series to the data while filtering/replacing outliers with values determined by the Fourier transform.

This routine is written in the IDL language. Its source code can be found in the file TS_HANTS.pro in the lib subdirectory of the IDL distribution.

Examples

; Define an n-element vector of time-series samples:
range = [0:4*!pi:.1]

data = SIN(range) + RANDOMU(seed, range.length)

hants = TS_HANTS(data)

                
; Compute the harmonic analysis of the time-series:

 pd = PLOT( data, NAME = 'Original Data' )

ph = PLOT( hants, 'r', NAME = 'HANTS Data', /OVERPLOT )

l = LEGEND( TARGET = [pd,ph], /AUTO_TEXT_COLOR )

IDL plots:

Syntax

Result = TS_HANTS( X[, AMPLITUDE=value] [, DELTA=value] [, DOD=value] [,/DOUBLE] [, ERR_TOLERANCE=value] [, /HIGH] [, /LOW] [, NUM_FREQUENCIES=value] [, NUM_PERIOD=value] [, PHASES=value] [, RANGE_MAXIMUM=value] [, RANGE_MINIMUM=value] [, TIME_SAMPLE=value] [, NUM_IMAGES=value] )

Return Value

The result is an n-element vector of the same data type as the input vector.

Arguments

X

An n-element single- or double-precision floating-point vector containing the reconstructed time-series.

Keywords

AMPLITUDE

Output variable. An array of amplitudes describing the Fourier transform, where the first element is the average of the curve.

DELTA

A scalar number which will be used to suppress high amplitudes.

DOD

The degree of overdeterminedness. The iteration of the code will stop if the number of points reaches the minimum required for curve fitting, plus the DOD.

DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

ERR_TOLERANCE

The error tolerance for the curve fitting. Points deviating more than ERR_TOLERANCE are rejected.

HIGH

Set this keyword to reject outliers which lie above the fitted curve.

LOW

Set this keyword to reject outliers which lie below the fitted curve.

NUM_FREQUENCIES

The number of frequencies to be considered above the zero frequency.

NUM_PERIOD

Length of the base period. Measured in virtual samples.

PHASES

Output variable. An array of phases describing the Fourier transform, where the first element is zero.

RANGE_MAXIMUM

The maximum value to consider, all other values higher are rejected.

RANGE_MINIMUM

The minimum value to consider, all other values lower are rejected.

TIME_SAMPLE

Array of size NUM_IMAGES which give a values of a virtual sample relative to the base period.

NUM_IMAGES

The total number of acual samples in the time series.

Version History

8.4	Introduced