Convolutional neural networks (CNNs) are widely used for image recognition and text analysis, and have been suggested for application on one-dimensional data as a way to reduce the need for pre-processing steps. Pre-processing is an integral part of multivariate analysis, but determination of the optimal pre-processing methods can be time-consuming due to the large number of available methods. In this work, the performance of a CNN was investigated for classification and regression analysis of spectral data. The CNN was compared with various other chemometric methods, including support vector machines (SVMs) for classification and partial least squares regression (PLSR) for regression analysis. The comparisons were made both on raw data, and on data that had gone through pre-processing and/or feature selection methods. The models were used on spectral data acquired with methods based on near-infrared, mid-infrared, and Raman spectroscopy. For the classification datasets the models were evaluated based on the percentage of correctly classified observations, while for regression analysis the models were assessed based on the coefficient of determination (R$^2$). Our results show that CNNs can outperform standard chemometric methods, especially for classification tasks where no pre-processing is used. However, both CNN and the standard chemometric methods see improved performance when proper pre-processing and feature selection methods are used. These results demonstrate some of the capabilities and limitations of CNNs used on one-dimensional data.