4.3: Cleaning Up Signals and Counting Events
- Page ID
- 407090
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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.
![Example of signal when counting number of events in a defined period of time.](https://chem.libretexts.org/@api/deki/files/417428/raw_signal.png?revision=1&size=bestfit&width=313&height=322)
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.
![Effect of threshold voltage on digitization of data.](https://chem.libretexts.org/@api/deki/files/417429/signal_shaper.png?revision=1&size=bestfit&width=522&height=587)
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.
![Operation of a binary pulse counter.](https://chem.libretexts.org/@api/deki/files/417432/binary_pulse_counter.png?revision=1&size=bestfit&width=930&height=296)