## Power and sensitivity measured at the correlator output for one baseline

After the atmopheric calibration that converts the measurement scale from the correlator output (in counts) to the scale, the output of the correlator for one correlation is a power equivalent temperature (in the Rayleigh-Jeans domain), which is sampled at a rate of , where is the frequency bandwidth over which the power is measured. As explained in the Sect. , the standard deviation of each power measurement is given by the system temperature power ( ). During the integration time ( ), independent samples of the signal power are measured to ensure the Nyquist sampling of the signal in the bandwidth . The signal power is averaged over these independent samples. The uncertainty on the averaged signal power, named sensitivity ( ), is thus standard deviation of the average or

| (1)

One subtlety is that the system temperature characterize one baseline between, eg., antennas and . Instead of just , we should write in all generality with

| (2)

where and are the single dish system temperature of antenna and . For simplicity, we will keep the notation hereafter.