4.3: Cleaning Up Signals and Counting Events

How an instrument handles signals depends on what is being measured, so we cannot develop here a single model that applies to all instruments. Broadly speaking, however, an instrument is likely to include one or more of the following: the ability to clean up the raw signal and convert it into a form that we can analyze; the ability to count events in binary form; the ability to convert binary information into a digital information; and the ability to convert between digital and analog signals. In this section we will cover the first two of these topics.

Cleaning Up a Signal

Suppose our instrument is designed to count discrete events, perhaps a Geiger counter that detects the emission of \(\beta\) particles, or a photodiode that detects photons. Even though a time-dependent count of particles is a digital signal, the raw signal (a voltage) likely consists of digital pulses superimposed on a background signal that contains noise, as seen in Figure \(\PageIndex{1}\). The total signal, therefore, is in analog form.

Figure \(\PageIndex{1}\). The raw signal (voltage) for an experiment in which we are interested in counting the number of events in a defined period of time. In this case, there are five discrete pulses, two of which partially overlap each other. The individual pulses are superimposed on a background signal that shows a modest amount of random noise.

To clean up this signal we want to accomplish two things: remove the noise and ensure that each pulse is counted. A simple way to accomplish this is to set a threshold signal and use a voltage follower operational amplifier (see Chapter 3) to set all voltages below the threshold to a logical value of 0 and all voltages above the threshold to a logical value of 1. As seen in Figure \(\PageIndex{2}\), the choice of the threshold voltage must be chosen carefully if we are to resolve closely spaced pulses and discriminate against noise. Note that the peak-shaped pulses become rectangular pulses.

Figure \(\PageIndex{2}\). Two attempts at cleaning up the data from Figure \(\PageIndex{1}\). At the top, setting the threshold voltage to 5 results in a noise-free set of rectangular pulses that are well-separated from each other. Setting the threshold to 0.5 volts merges the two separate pulses at times between 1.0 and 1.5 into a single pulse and captures a number of noise spikes between times of 1.5 and 2.0, and between times of 2.5 and 3.0.

Binary Pulse Counter

To count the pulses in Figure \(\PageIndex{2}\) we can send them though a binary pulse counter (BPC). Figure \(\PageIndex{3}\) shows how such a counter works. In this case, the BPC has three registers, each of which can be in a logical state of 0 or 1. With three registers, we are limited to counting no more than \(2^3 = 8\) pulses; a more useful BPC would have more registers. We can treat the pulses as entering the BPC from the right. When a pulse enters a register, it flips each register from 1 to 0 or from 0 to 1, stopping after if first flips a register from 0 to 1. For example, the second pulse flips the right-most register from 1 to 0 and the middle register from 0 to 1; because the middle register initially was at 0, the counting of this pulse comes to an end.

Figure \(\PageIndex{3}\). Operation of a binary pulse counter showing how the contents of three registers respond to the measurement of five pulses.