For a pulsar search observation, with the two polarizations averaged, a useful rule of thumb can be given for calculating the expected rms noise. If the rms noise, $\sigma$, is expressed in terms of the flux density of the target pulsar, then;

             $\sigma = \frac{{\rm T}_{sys}}{G \sqrt{2 \beta \tau}}
\left( \frac{w}{{\rm P} - w} \right)^{0.5} {\rm Jy} $

Where, ${\rm T}_{sys}$ is the system temperature, including the contributions from the celestial background and, if appropriate, any continuum emission from a host supernova remnant, etc., $G$ is the telescope gain (in K/Jy), $\beta$ is the system bandwidth, $\tau$ is the total integration time of the observation, P is the pulsar period, and w is the effective duration of the pulsar pulse.

Robert Minchin 2017-10-30