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cubicwgt


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 -- Function File: A = cubicwgt (SERIES)

     Returns the input series, windowed by a polynomial similar to a
     Hanning window.  To window an arbitrary section of the series,
     subtract or add an offset to it to adjust the centre of the window;
     for an offset of k, the call would be cubicwgt (S - k).  Similarly,
     the radius of the window is 1; if an arbitrary radius r is desired,
     dividing the series by the radius after centering is the best way
     to adjust to fit the window: cubicwgt ((S - k) / r).

     The windowing function itself is: w = 1 + ( x ^ 2 * ( 2 x - 3 ) ),
     x in [-1,1], else w = 0.


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Returns the input series, windowed by a polynomial similar to a Hanning
window.



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lombcoeff


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 -- Function File: C = lombcoeff (TIME, MAG, FREQ)

     Return the Lomb Periodogram value at one frequency for a time
     series.

     See also: lombnormcoeff.


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Return the Lomb Periodogram value at one frequency for a time series.



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lombnormcoeff


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 -- Function File: C = lombnormcoeff (TIME, MAG, FREQ)

     Return the normalized Lomb Periodogram value at one frequency for a
     time series.

     See also: lombcoeff.


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Return the normalized Lomb Periodogram value at one frequency for a time
seri...



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lscomplex


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 -- Function File: T = lscomplex (TIME, MAG, MAXFREQ, NUMCOEFF,
          NUMOCTAVES)

     Return a series of least-squares transforms of a complex-valued
     time series.  Each transform is minimized independently at each
     frequency.  NUMCOEFF frequencies are tested for each of NUMOCTAVES
     octaves, starting from MAXFREQ.

     Each result (a + bi) at a given frequency, o, defines the real and
     imaginary coefficients for a sum of cosine and sine functions: a
     cos(ot) + b i sin(ot).  The specific frequency can be determined by
     its index in T, IND, as MAXFREQ * 2 ^ (- (IND - 1) / NUMCOEFF).

     See also: lsreal.


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Return a series of least-squares transforms of a complex-valued time
series.



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lscomplexwavelet


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 -- Function File: T = lscomplexwavelet (TIME,
     MAG, MAXFREQ, NUMCOEFF, NUMOCTAVE, MIN_TIME, MAX_TIME, STEP_TIME,
     SIGMA


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MAG, MAXFREQ, NUMCOEFF, NUMOCTAVE, MIN_TIME, MAX_TIME, STEP_TIME, SIGMA



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lscorrcoeff


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 -- Function File: C = lscorrcoeff (TIME1, MAG1, TIME2, MAG2, TIME,
          FREQ)
 -- Function File: C = lscorrcoeff (TIME1, MAG1, TIME2, MAG2, TIME,
          FREQ, WINDOW = CUBICWGT)
 -- Function File: C = lscorrcoeff (TIME1, MAG1, TIME2, MAG2, TIME,
          FREQ, WINDOW = CUBICWGT, WINRADIUS = 1)

     Return the coefficient of the wavelet correlation of two complex
     time series.  The correlation is only effective at a given time and
     frequency.  The windowing function applied by default is cubicwgt,
     this can be changed by passing a different function handle to
     WINDOW, while the radius applied is set by WINRADIUS.  Note that
     this will be most effective when both series have had their mean
     value (if it is not zero) subtracted (and stored separately); this
     reduces the constant-offset error further, and allows the functions
     to be compared on their periodic features rather than their
     constant features.

     See also: lswaveletcoeff, lscomplexwavelet, lsrealwavelet.


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Return the coefficient of the wavelet correlation of two complex time
series.



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lsreal


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 -- Function File: T = lsreal (TIME, MAG, MAXFREQ, NUMCOEFF, NUMOCTAVES)

     Return a series of least-squares transforms of a real-valued time
     series.  Each transform is minimized independently for each
     frequency.  The method used is a Lomb-Scargle transform of the
     real-valued (TIME, MAG) series, starting from frequency MAXFREQ and
     descending NUMOCTAVES octaves with NUMCOEFF coefficients per
     octave.

     The result of the transform for each frequency is the coefficient
     of a sum of sine and cosine functions modified by that frequency,
     in the form of a complex number—where the cosine coefficient is
     encoded in the real term, and the sine coefficient is encoded in
     the imaginary term.  Each frequency is fit independently from the
     others, and to minimize very low frequency error, consider storing
     the mean of a dataset with a constant or near-constant offset
     separately, and subtracting it from the dataset.

     See also: lscomplex.


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Return a series of least-squares transforms of a real-valued time
series.



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lsrealwavelet


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 -- Function File: t = lsrealwavelet( TIME, MAG,
     MAXFREQ, COEFFICIENTS, OCTAVES, TIME_MIN, TIME_MAX,
     MIN_WINDOW_COUNT )

     Computes a windowed transform of the supplied (TIME, MAG) series of
     real-valued magnitudes, applying progressively wider windows as the
     frequencies tested decline from the maximum frequency.

     Currently non-functional.

     See also: lscomplexwavelet, lswaveletcoeff, lscorrcoeff.


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MAXFREQ, COEFFICIENTS, OCTAVES, TIME_MIN, TIME_MAX, MIN_WINDOW_COUNT )



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lswaveletcoeff


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 -- Function File: C = lswaveletcoeff (T, X, TIME, FREQ)
 -- Function File: C = lswaveletcoeff (T, X, TIME, FREQ,
          WINDOW=cubicwgt)
 -- Function File: C = lswaveletcoeff (T, X, TIME, FREQ,
          WINDOW=cubicwgt, WINRADIUS=1)

     Return the wavelet transform of a complex time series in a given
     window.  The transform takes a complex time series (T, X) at time
     TIME and frequency FREQ, then applies a windowing function to it;
     the default is cubicwgt, however by providing a function handle for
     the optional variable WINDOW, the user may select their own
     function; to determine the radius of the interval around the TIME
     selected, set WINRADIUS to some value other than 1.

     This transform operates identically to the transform at the heart
     of lscomplexwavelet, however for one window only.

     See also: lscorrcoeff, lscomplexwavelet, lsrealwavelet.


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Return the wavelet transform of a complex time series in a given window.





