Correlation and delay line attenuation

The effect of delay line attenuation on the output of a correlator is studied for the case where the attenuation in db to within a frequency independent loss varies linearly with delay and as the square root of frequency. It is shown how attenuation affects the output signal-noise ratio of the correlator, increasing it for some signal spectrum shapes and decreasing it for others. Upper bounds on the increase and decrease are computed and a sufficient condition on the input signal spectrum is established which, when satisfied, assures a degradation in signal-noise ratio. Also examined is the effect of a frequency independent gain inserted to compensate for the delay line attenuation. It is shown how this gain may be chosen in order to give uniform system output noise over all values of delay.