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Averaging Scans

A great many experiments need the ability to average a number of scans together, for example those taken on the same position. UniPOPS provides a convenient system for achieving this via the verbs ACCUM and SUM.

Averaging Scans with Default Weighting

When ACCUM is invoked, the scan in Array (0) is summed into an internal array. In LINE, a weighting factor is applied that is proportional to the integration time, and inversely proportional to the square of the system temperature (the values of these two parameters being taken from the scan header. For Green Bank data, UniPOPS uses effective integration times while for 12-m data it uses scan duration time). Currently, the weighting factor in CONDAR is unity.

The order of operations involved in the simplest possible averaging of data with ACCUM is,

You set the accumulator flag to OFF by invoking the verb SCLEAR. (This flag is set to ON when averaging is in progress.)
You place the first scan to be summed into Array (0), and invoke ACCUM. ACCUM sets the accumulator flag to ON, and copies the header values of the scan into the internal array. ACCUM also copies the data values after multiplying by the weighting factor described above.
You place the successive scans to be averaged in Array (0), and call ACCUM. This adds the new scan into the sum in the internal array, after multiplication by the appropriate weighting factor. The sum of the weights is also retained.
When the final scan has been ACCUMed, you invoke the verb AVE. This normalizes the sum in the internal array by the sum of the weights, and copies the normalized summation back to Array (0). AVE sets the accumulator flag to OFF.
If at any stage you type,
```
		>TELL ACCMD
```
then before invoking AVE, the list of scans ACCUMed to date will be printed. After invoking AVE, the number of scans ACCUMed and the scan numbers of the first and last component scans are printed on the screen.

NOTE :

In LINE, the final average in Array (0) will have the basic header of the first scan ACCUMed, but the integration times (keyword adverbs INTTIME and EFFINT) will be the sum of the integration times of the individual scans, while the system temperature (keyword adverb STSYS) will be the weighted mean of the values for the individual scans.

NOTE :

The behavior of ACCUM with respect to undefined data values (data values equal to IEEE Inf) is determined by the value of the DEFMODE adverb. If DEFMODE is FALSE, the result of each ACCUM will have an undefined value in the internal accum array at any location where either of the values in the scan being ACCUMed or the current internal accum are have an undefined value (in this case, once a channel has an undefined value in the internal accum array, it will remain undefined). If DEFMODE is TRUE, the result of each ACCUM will have an undefined value at any location where both of the values in the scan being ACCUMed and the current internal accum array have undefined values but if only one values is undefined at a location, ACCUM will use that value as the result at that location. The value of DEFMODE can be changed at any time. The default value of DEFMODE is FALSE and most users will not change this value.

As an example, suppose it is desired to average scans 602, 604 and 606, then type,

	>SCLEAR
	>GET 602; ACCUM
	>GET 604; ACCUM
	>GET 606; ACCUM
	>AVE

To see what has gone on, and then display the averaged scan, type,

	>TELL ACCMD
	>PAGE SHOW

Averaging Scans with User-Specified Weights

On occasions, you may wish to specify the weights used in averaging the scans together. To achieve this, you should enter the weight for each scan into the adverb WEIGHT, and invoke the verb SUM (rather than ACCUM).

Suppose you wished to repeat the above averaging of scans 602, 604 and 606, but using weights inversely proportional to the rms's of each scan. Employing the verb RMS, (see Section 7.6) and its adverb VRMS, type,

	>SCALAR I
	>SCLEAR
	>FOR I = 602 TO 606 BY 2; GET I; RMS; WEIGHT = 1./VRMS; SUM; END
	>AVE
	>TELL ACCMD
	>PAGE SHOW

Note: SUM uses the adverb DEFMODE in the same sense that ACCUM does. See the note at the end of Section 10.1 for more information.

Averaging Scans with Frequency, Velocity or Position Offsets

The case can arise in which spectra of the same resolution, containing the same line, have frequency or radial velocity offsets relative to each other, but it is desired to sum all after suitable alignment. It is possible to align these, despite the offsets, using the verbs FSHIFT, VSHIFT, and SHIFT. The verbs FSHIFT and VSHIFT set the adverb ASHIFT to the number of channels by which the spectrum must be shifted, and this is used by SHIFT to align the scans. You can specify the channel shifts yourself by setting the values of ASHIFT by assignment statements (i.e. ASHIFT = 35.). This is also done when you desire to average continuum scans having offset starting points in CONDAR, only here ASHIFT is set to the required shift in pixels. Note that if ASHIFT is not an integer number, then appropriate interpolation of the scan will be performed.

If scans 602, 604 and 606 had been observed with different frequency offsets, then they should be averaged by typing,

	>SCLEAR
	>GET 602 ACCUM
	>GET 604 FSHIFT SHIFT ACCUM
	>GET 606 FSHIFT SHIFT ACCUM
	>AVE PAGE SHOW

NOTE : In the regions of the summed scans, where not all scans overlap, you should not trust the result ! In making the final plot, BDROP and EDROP should be used to mask out these bogus sections of the scan.

SHIFT also updates an internal record of the number of channels shifted. Up to the last 5120 values and the scan numbers associated with them can be displayed using the LISTSHIFT verb. The SCLEAR verb clears this internal record.

NOTE: For Tucson 12-meter data only, there is a verb OSB which, when invoked, changes several header words to make the data appear as if it had been observed in the other side band with the velocity at the reference channel remaining the same. A subsequent use of OSB will return these header values to their original settings. OSB also sets the OPENPAR header value to "OSB" if it is unset, or to " " if it is set to "OSB". SHOW and HEADER display this string if it is set.

Using the Stack when Averaging Data

Averaging a large number of scans is an operation where the stack (see Chapter 11) can be used to aid the process considerably. For example, if it is desired to average the spectra in scans 602, 604 and 606, plus scans 1000 through 1020, this is easily achieved using the stack by typing,

	>SCALAR I
	>EMPTY
	>ADDSTACK(602,606,2)
	>ADDSTACK(1000,1020,1)
	>SCLEAR
	>FOR I = 1 TO ACOUNT; GET ASTACK(I); ACCUM; END
	>AVE
	>TELL ACCMD
	>PAGE SHOW

To see exactly which scans have been averaged, one can print out the stack by typing,

	>TELL STACK

As a further example, if the frequency resolutions of a set of spectra entered on the stack (see Chapter 11) differ, the following procedure will shift all scans for frequency offsets, smooth them to the resolution of the first scan, where possible, (alerting you if this is not possible), and average the smoothed, shifted scans,

	>PROCEDURE SMTHSHFT
	:SCALAR I_LOOP
	:IF ACOUNT < 2 THEN
	:	PRINT 'THE STACK IS EMPTY OR CONTAINS BUT ONE SCAN !"
	:	RETURN
	:	END
	:SCLEAR
	:GET ASTACK(1); ACCUM
	:FOR I_LOOP = 2 TO ACOUNT
	:	GET ASTACK(I_LOOP)
	:	NEWRES = H0(FREQRES)/H2(FREQRES)
	:	IF NEWRES >= 1. THEN
	:		CHNGRES
	:		FSHIFT SHIFT ACCUM
	:	ELSE
	:		PRINT 'CANNOT SMOOTH', ASTACK(I_LOOP)
	:	END
	:END
	:AVE
	:RETURN
	:FINISH

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