
Spectral Resolution and Sensitivity Bandwidth in SpectrometersFor many of the spectrometers used at millimeterwavelength observatories (filter bank spectrometers, correlation spectrometers, etc.), the true bandwidth of a single spectrometer channel is a convolution of the original gain response of the channel and any smoothing functions applied. This convolution of the response and smoothing functions affects two important factors:
The sensitivity bandwidth is defined as follows:
Kraus (Radio Astronomy, 2^{nd} Edition, page 78) defines a similar term. Table D.1 describes the relationship between, , and the frequency sampling for various smoothing functions F(v) assuming Nyquist sampling at . At the end of this Appendix I show the calculation for each of these integrals.
For the filter bank spectrometers at the 12m, the channel response is a second order Chebyshev bandpass filter (which approximates a pill box function), there is no smoothing, and they are not Nyquist sampled. A single channel in the Millimeter Autocorrelator (MAC), on the other hand, has a sinc frequency response which is hanning smoothed. Since the convolution of a sinc with any function that is already bandlimited within the frequency response of the sinc leaves that function unchanged, we are left with a hanning function response. Therefore:
D.1 Function IntegralsD.1.1 Sinc
D.1.2 Gaussian
D.1.3 HanningThe Hanning function is nonzero only from –(N – 1) to N – 1, where N is the number of channels which are being smoothed…
Normally, we take 3 channels and give them weights 0.25,0.5,0.25. Therefore, becomes
D.1.4 Hamming
The Hamming function is just the Hanning function with different weighting.

Copyright Arizona Radio Observatory. 