This paper focuses on the computation of stationary curves, which are sometimes called fingerprints for one dimensional real signals in the linear scale space. Images for the analysis in the linear scale space are expressed as digital images for each quantized scale. Therefore, we develop a discrete version of the linear scale space analysis, employing the results of digital image analysis. For the application of linear scale space analysis to the time-varying images and objects, our method has advantages, because our method is based on the digital geometry on a plane which is suitable for the computation in digital computers.