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### TS_HANTS

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