The fundamental concepts of noise and signal-to-noise ratio are central to the discipline of analytical chemistry. Since chemical instrumentation dominates the modern laboratory, it is critical that students understand the role noise plays in limiting the precision of a measurement. It is equally important that they understand how to implement active and passive means to mitigate noise. The purpose of this Mathcad document is to allow the student to gain a familiarity with the concepts of signal-to-noise ratios and to explore the advantages of ensemble averaging and digital filtering analytical signals. Simulated noisy signals are used to guide the student through a series of individual exercises (Fig. 1). These exercises culminate in a capstone experience where they simultaneously apply all of the concepts.

Figure 1. Ensemble averaged signal and original signal.