The Gaussian filter is set to remain of enduring importance in metrology. This publication deals with the digital implementation of the Gaussian filter and the estimation of the occurring errors. Guidance is given on how to keep these errors as small as possible. In addition algorithms for the implementation of the Gaussian filter are given. Contents: Specification of the Gaussian filter // Implementation by discrete convolution // Using the discrete Fourier transformation // Truncation effects // Sampling effects // Notes concerning the implementation // Reference algorithms.