Fibre Bragg gratings are one of the most popular sensors with a huge number of applications. Their most important advantage is signal modulation consisting in shifting the spectrum in the wavelength domain. Determining the wavelength shift is the most important issue in precise measurements of various quantities. New demodulation methods are constantly being developed. Many of them have good properties, but they do not gain much polarity. This is partly due to their high complexity and partly to a small improvement in the accuracy of determining the wavelength shift in relation to classical methods. Cumulative preprocessing is a very simple method of spectrum processing with the property of reducing the influence of noise on the result. The method can be used directly or with additional algorithms. In this article, we demonstrate the advantages of this method and the possibilities of combining it with other signal processing methods. We show that this method is much simpler than the spectrum denoising methods and additionally simplifies the next stage of the algorithm, i.e., determining the wavelength shift itself.