Most measurement techniques have some limitations imposed by a sensor's signal-to-noise ratio (SNR). Thus, in analytical chemistry, methods for enhancing the SNR are of crucial importance and can be ensured experimentally or established via pre-treatment of digitized data. In many analytical curricula, instrumental techniques are given preference as proper data generation is most important. Nonetheless, the ultimate goal is to utilize computational improvements as well and thus students need to be trained in data pre-treatment tools. This requires teaching a rather extensive math background for which there is a lack of concise teaching materials tuned to analytical chemistry. To overcome this hindrance, three methods for data filtering are presented: Savitzky-Golay smoothing, Fourier filtering, and the more recent and powerful wavelet filtering. By means of 1D signals as acquired with standard instrumentation for optical spectroscopy or chromatography and so forth, the basic principles are discussed and demonstrated. These methods are then expanded towards noise filtering of 2D data sets as obtained in microscopy or the upcoming chemical imaging as well as towards 3D data from spectroscopic imaging. In an extensive Supporting Information section, suggestions on introducing Fourier and wavelet transforms in lectures are presented. To support such lectures by visual demonstrations and hands-on learning, a windows-based software package, DENOISE.exe, has been developed and made available along with the simulated and real-world data used in this article. Because data are imported into DENOISE.exe as ASCII text files, the program can be utilized for any data sets an instructor may want to use. (Contains 13 figures and 4 notes.)