Feature extraction methods for sound events have been traditionally based on parametric representations specifically developed for speech signals, such as the well-known Mel Frequency Cepstrum Coefficients (MFCC). However, the discrimination capabilities of these features for Acoustic Event Classification (AEC) tasks could be enhanced by taking into account the spectro-temporal structure of acoustic event signals. In this paper, a new front-end for AEC which incorporates this specific information is proposed. It consists of two different stages: short-time feature extraction and temporal feature integration. The first module aims at providing a better spectral representation of the different acoustic events on a frame-by-frame basis, by means of the automatic selection of the optimal set of frequency bands from which cepstral-like features are extracted. The second stage is designed for capturing the most relevant temporal information in the short-time features, through the application of Non-Negative Matrix Factorization (NMF) on their periodograms computed over long audio segments. The whole front-end has been evaluated in clean and noisy conditions. Experiments show that the removal of certain frequency bands (which are mainly located in the medium region of the spectrum for clean conditions and in low frequencies for noisy environments) in the short-time feature computation process in conjunction with the NMF technique for temporal feature integration improves significantly the performance of a Support Vector Machine (SVM) based AEC system with respect to the use of conventional MFCCs.