Neuro-oncologists must ultimately rely on their acquired knowledge and accumulated experience to undertake the sensitive task of brain tumour diagnosis. This task strongly depends on indirect, non-invasive measurements, which are the source of valuable data in the form of signals and images. Expert radiologists should benefit from their use as part of an at least partially automated computer-based medical decision support system. This paper focuses on Magnetic Resonance Spectroscopy signal analysis and illustrates a method that combines Gaussian Decomposition, dimensionality reduction by Moving Window with Variance Analysis and classification using adaptively regularized Artificial Neural Networks. The method yields encouraging results in the task of binary classification of human brain tumours, even for tumour types that have seldom been analyzed from this viewpoint.