For a better understanding of the biology of an organism, a complete description is needed of all regions of the genome that are actively transcribed. Tiling arrays are used for this purpose. They allow for the discovery of novel transcripts and the assessment of differential expression between two or more experimental conditions such as genotype, treatment, tissue, etc. In tiling array literature, many efforts are devoted to transcript discovery, whereas more recent developments also focus on differential expression. To our knowledge, however, no methods for tiling arrays have been described that can simultaneously assess transcript discovery and identify differentially expressed transcripts. In this paper, we adopt wavelet based functional models to the context of tiling arrays. The high dimensionality of the data triggered us to avoid inference based on Bayesian MCMC methods. Instead, we introduce a fast empirical Bayes method that provides adaptive regularization of the functional effects. A simulation study and a case study illustrate that our approach is well suited for the simultaneous assessment of transcript discovery and differential expression in tiling array studies, and that it outperforms methods that accomplish only one of these tasks.