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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.





