The Workings of Pulse-Height Discrimination
Pule Height Analaysis (PHA) is done on the current pulse from the detector. It only works for detectors which have a current pulse which is proportional to the energy of the x-ray (scintillation counters and gas proportional counters). It does not work for Geiger counters where the current pulse doesn't depend on the x-ray energy.  

Think of dropping the current through a resistor. The current pulse then has a voltage. Basically you set a low and a high voltage (a window) for the detector pulses which you will count. Any detector signals within the window are counted, those outside the window (too low or too high) are rejected. 

Given that the detector current (or voltage really) should be proportional to the energy of the x-ray detected this improves the S/N ratio. So "low" current pulses don't have enough energy to be a Cu K-alpha x-ray, and high energy pulses have too much energy. High pulses could be for example an x-ray with twice the energy.

It is important to note that the rejected pulses are not "background" counts per se. But there is a twist. The rejected pulses do create detector deadtime. So you have to be careful that the overall count rate of the detector is low enough to still be linear, or do a correction for the total count rate.