Sooo I wasn't sure if I should put this here or in the astrophysics section, but I figured electrical engineering was more relevant for my question.(adsbygoogle = window.adsbygoogle || []).push({});

I'm involved in a project at my university to build a (very) simple radio telescope, but I'm having a bit of trouble with the radiometer equation:

[itex]\sigma_T \approx \dfrac{T_{sys}}{\sqrt{\Delta \nu_{RF} \cdot \tau}}[/itex]

Where [itex]\sigma_T[/itex] is the "sensitivity" or the minimum detectable temperature, [itex]T_{sys}[/itex] is the system temperature, [itex]\Delta \nu_{RF}[/itex] is the bandwidth, and [itex]\tau[/itex] is the integration time.

I'm mostly having trouble with "integration time". This seems to imply that one has to use an integrating analog to digital converter (something like a dual-slope ADC I guess...), but this seems to prevent the application of Fourier analysis (am I wrong in thinking this?). However, I have seen some examples of radiometers that appear to take discrete samples, and apply some sort of "integration time".

Since the product [itex]\nu \cdot \tau[/itex] is effectively the number of samples that would have been taken over the integration time, I was wondering if this product could equated to some function of sample rate of a non-integrating ADC?

Rereading my above questions, they aren't the most coherent sentences in the world... But I'm not quite sure how else to pose them. I have a feeling I'm overthinking this, or missing something simple. If anyone needs anything clarified, please let me know!

Thanks so much for the help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Radio astronomy - integration time vs. sample rate

**Physics Forums | Science Articles, Homework Help, Discussion**