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Signal-to-noise enhancement is an important topic to cover in any undergraduate instrumental analysis course. With the ubiquity of electronic chemical instrumentation, students who want to understand the construction of instruments must understand the nature of an electronic signal and how it is transduced into a form that is understood by a human operator. An important and relevant component of signal-to-noise enhancement is digital filtering. While digital filters are discussed in most instrumental analysis textbooks, their numerically intensive nature makes them difficult to include in a student exercise in any way except pictorially. This type of exercise does not let students interact with the filtering process to actually see how it works.
The FTDigitalFilter.xls file is constructed to allow the user to change the parameters of a simulated digital filter and see the effect the filtering has on a noisy signal. The spreadsheet consists of two sheets that demonstrate the efficacy of a Fourier Transform (FT) frequency-domain square-wave apodization filter on a signal containing environmental noise (two single-frequency noise sources) or a white noise source. In the “Environ Noise” sheet, the user can set the frequency of the signal, the frequency of two single-frequency sources of noise, the amplitude of the noise, and the size of the apodization window. After the FT filter is performed with the push of a button, a time-domain graph containing the pure signal, noisy signal, and filtered signal is presented along with a frequency-domain graph containing the unfiltered and filtered signals. In the white noise example, the procedure is the same except the only noise parameter is the amplitude of the white noise.
Screen shot of the "Environ Noise" sheet shwing the time and frequency-domain graps of the signal.
The Signal-to-Noise Ratio (SNR) is calculated before and after the digital filtering process in order to provide a quantitative means of comparing the efficacy of the filtering method. The SNR is calculated by dividing the peak-to-trough amplitude of the pure signal by the standard deviation of the noise generated.
A more thorough treatment of digital filtering using Microsoft Excel can be found in de Levie’s book, Advanced Excel for Scientific Data Analysis(1).
Literature Cited
- de Levie, R. Advanced Excel for Scientific Data Analysis; Oxford: New York, 2004; pp 245–255.
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