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      Apply a least-squares (Savitzky-Golay) polynomial smoothing filter


      Reduce noise in 1-D data (e.g. time-series, spectrum) but retain
      dynamic range of variations in the data by applying a least squares
      smoothing polynomial filter,
      Also called the Savitzky-Golay smoothing filter, cf. Numerical
      Recipes (Press et al. 1992, Sec.14.8)
      The low-pass filter coefficients are computed by effectively
      least-squares fitting a polynomial in moving window,
      centered on each data point, so the new value will be the
      zero-th coefficient of the polynomial. Approximate first derivates
      of the data can be computed by using first degree coefficient of
      each polynomial, and so on. The filter coefficients for a specified
      polynomial degree and window width are computed independent of any
      data, and stored in a common block. The filter is then convolved
      with the data array to result in smoothed data with reduced noise,
      but retaining higher order variations (better than SMOOTH).
      This procedure became partially obsolete in IDL V5.4 with the
      introduction of the SAVGOL function, which computes the smoothing

Calling Sequence

      spectrum = poly_smooth( data, [ width, DEGREE = , NLEFT = , NRIGHT =
                                      DERIV_ORDER = ,COEFF = ]


      data = 1-D array, such as a spectrum or time-series.
      width = total number of data points to use in filter convolution,
              (default = 5, using 2 past and 2 future data points),
              must be larger than DEGREE of polynomials, and a guideline is to
              make WIDTH between 1 and 2 times the FWHM of desired features.

Optional Input Keywords

      DEGREE = degree of polynomials to use in designing the filter
              via least squares fits, (default DEGREE = 2)
              The higher degrees will preserve sharper features.
      NLEFT = # of past data points to use in filter convolution,
              excluding current point, overrides width parameter,
              so that width = NLEFT + NRIGHT + 1. (default = NRIGHT)
      NRIGHT = # of future data points to use (default = NLEFT).
      DERIV_ORDER = order of derivative desired (default = 0, no derivative).

Optional Output Keyword

      COEFFICIENTS = optional output of the filter coefficients applied,
              but they are all stored in common block for reuse, anyway.


      Function returns the data convolved with polynomial filter coefs.


      Given a wavelength - flux spectrum (w,f), apply a 31 point quadratic
      smoothing filter and plot
      IDL> cgplot, w, poly_smooth(f,31)

Common Blocks

      common poly_smooth, degc, nlc, nrc, coefs, ordermax


      As described in Numerical Recipies, 2nd edition sec.14.8,
      Savitsky-Golay filter.
      Matrix of normal eqs. is formed by starting with small terms
      and then adding progressively larger terms (powers).
      The filter coefficients of up to derivative ordermax are stored
      in common, until the specifications change, then recompute coefficients.
      Coefficients are stored in convolution order, zero lag in the middle.

Modification History

      Written, Frank Varosi NASA/GSFC 1993.
      Converted to IDL V5.0 W. Landsman September 1997
      Use /EDGE_TRUNCATE keyword to CONVOL W. Landsman March 2006

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