CMPLXFILT-Create a mid-pass filter for complex data

Description:

CMPLXFILT generates a complex data structure whose data have the form of a mid-pass filter that can be applied to other complex data of the same size using CMPLXMULT. The filter is specified by a low and high cutoff. If the low cutoff is specified as 0, a low-pass filter is constructed.

Parameters:

CDATA

CMPLXFILT uses an input complex data structure, specified as CDATA, as a template for the filter it generates. The resulting filter has the same structure (and data dimem- sions) as the template, only the data arrays differing. If the template data is n-dimensional, an n-dimensional filter will be generated, the cutoff frequencies being the same in each dimension.

LOWCUT

The mid-pass filter rises from zero, LOWCUT being the frequency (specified in terms of the Nyquist frequency) at which it reaches a height of exp(-1/2) = 0.6 If LOWCUT is specified as zero, a low-pass filter results. The filter is in fact a falling gaussian with a width specified by HICUT which has subtracted from it a rising gaussian with a width specified by LOWCUT.

HICUT

HICUT is the element at which the filter drops to a height of exp(-1/2) = 0.6 It is specified in terms of the Nyquist frequency.

OUTPUT

The name of the resulting filter. If OUTPUT is the same as CDATA, the filter replaces the data originally in CDATA. Otherwise, a new structure is created.

Source comments:

 C M P L X F I L T

 This routine produces a mid-pass complex filter, given a complex
 structure as a template and low and high cutoff values.  The
 filter is produced by the subtraction of two gaussians.  If no
 low value is specified, the result is a single gaussian low-pass
 filter.

 Command parameters -

 CDATA    (Character) The name of the template complex structure.
 LOWCUT   (Numeric) The low cutoff value for the filter.  This is
          specified in terms of the Nyquist frequency.  It is the
          sigma of the low cut gaussian, i.e. the point at which the
          rising edge of the filter reaches exp(-1/2) =~.6
 HICUT    (Numeric) The high cutoff value for the filter.  This is
          specified in terms of the Nyquist frequency.  It is the
          sigma of the high cut gaussian, i.e. the point at which the
          falling edge of the filter reaches exp(-1/2) =~.6
 OUTPUT   (Character) The name of the resulting structure.  This
          may be the same as CDATA, in which case the operation
          is performed in situ.  Otherwise, a new file is created.

 Command keywords - None

 Output data -

 The resulting complex data have a zero imaginary part, and a real
 part given by F(X)=exp(-X**2/(2*V**2))-exp(-X**2/(2*U**2))
 where U and V are the low and high frequency cutoffs respectively.
 (Note that the actual data generated is symmetrical about the
 mid point of the data, which is assumed to be the zero frequency
 - the Figaro function FFT produces data in this form).

                                     KS / AAO  9th Oct 1986.