The effect of digitisation on the signal-to-noise ratio of a pulsed radio signal

We discuss the effect of digitisation on the signal-to-noise ratio of pulsed radio signals. We describe a general n-bit digitiser and show that a symmetric and equidistant digitiser has two free parameters: the threshold and the output value. We derive the best choice of these values for a 1, 1.5, 2, 4 and 8-bit digitiser and calculate the signal-to-noise ratio after digitisation of an undetected signal and of a detected signal with a Gaussian or a chi (2)-distribution. Measurements made using PuMa, the new digital pulsar machine at the Westerbork Synthesis Radio Telescope, are presented and are shown to agree with the theoretical response of the digitiser.