DSN Radio Astronomy
Spectra Tcl Toolkit

Last updated by Tom Kuiper on 2000 Oct 5.

Date Storage and Retrieval
Spectrum Calibration & Averaging

Background

Spectrum Calibration
Spectrum Averaging
Normalized Spectra

Tcl Commands

spectrum_calibrate Calibrates a raw data spectrum

spectra_average Finds the average of two spectra

Data Storage and Retrieval

Data files are in FITS format
Data storage and retrieval is done with FitsTcl

New local FITS keywords have been defined to record the steps of converting autocorrelation functions to spectra, and calibrating the spectra:

ZERO-COR	= omit / perform / complete Correct DC bias in 1-bit autocorrelation functions
AC-NORM	= omit / perform / complete Normalize the autocorrelation function
CLIP-COR	= omit / perform / complete Apply clipping correction to 1-bit autocorrelation functions
FOURIER	= omit / perform / complete Fourier transform an autocorrelation function
SPECNORM	= omit / perform / complete Normalize a spectrum
TCAL-DIF	= omit / perform / complete Calibrate a power spectrum using a calibration noise source and the Sig-Ref difference method
TCAL-RAT	= omit / perform / complete Calibrate a difference spectrum using a calibration noise source and the Sig/Cal ratio method
TSYS-RAT	= omit / perform / complete Calibrate a difference spectrum using a system power spectrum and the Dif/Tsys ratio method
TSYS-DIF	= omit / perform / complete Calibrate a spectrum using a system power spectrum and the (Sig-Ref)/Ref method
CALSCALE	= omit / perform / complete Apply to appropriate scaling constant to a calibrated spectrum.
PROCSPEC	= complete This spectrum has been manipulated as recorded in the HISTORY keywords.
DATATYPE	= sig / ref / switched / amb-load /cal-source / zero Type of data in the spectrum,

Spectrum Calibration and Averaging

This section assumes that autocorrelation functions have been normalized (as discussed in the Spaceborne Tcl Toolkit) and ourier transformed, resulting in Tcl numeric lists containing normalized spectra, S.

Background

The derivations for calibration and averaging yield the following formulae:

Spectrum Calibration

The spectrum towards the source of interest, with any continuum emission removed, is

The effective integration time for the calibrated spectrum, assuming that the signal and reference spectra do not have the same integration times, is

so that the noise in the calibrated spectrum is

Averaging

If we have two spectra with unequal integration times and system temperatures, they can be combined so as to minimize the noise in the combined spectrum:

The effective integration time of the combined spectrum is

and the effective system temperature of the combined spectrum is obtained from

Normalized Spectra

Since the averaging of spectra requires that the system temperature associated with each spectrum be retained (as well as the integration time), it may be more convenient to store all spectra in normalized form, so that

In that case, the formula for calibrating spectra is

and for averaging spectra is

Tcl Package `spectra-0.1`

spectrum_calibrate data_spectrum reference_spectrum

Performs the operations described in eqs. 3 and 8 above. The spectra are Tcl lists consisting of

the integration time, and
a Tcl list with the spectrum data values.

spectra_average spectrum_1 spectrum_2

Performs the operations described in eqs. 17, 18 and 13 above. The spectra are Tcl lists consisting of

the integration time,
the system temperature,
and a Tcl list with the spectrum data values.

`spectrum_calibrate`	Calibrates a raw data spectrum
`spectra_average`	Finds the average of two spectra

DSN Radio AstronomySpectra Tcl Toolkit

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