In this paper, a speech recognition system is developed for recognizing speaker-independent, isolated words. Speech recognition is a fascinating application of Digital Signal Processing and is a pattern classification task wherein an input pattern is classified as a sequence of stored patterns that have previously been learned. Isolated words in Malayalam, which belong to one of the four Dravidian languages of Southern India, are used to create the database. Feature extraction in the time-frequency domain is performed using Wavelet Packet Decomposition (WPD). Artificial Neural Networks (ANNs) are used for training, testing and pattern recognition. Wavelets are very much suitable for processing non stationary signals like speech because of its multi-resolution characteristics and efficient time frequency localizations. Algorithms based on neural networks are well suitable for addressing speech recognition tasks. Recognition accuracy of 87.5% is obtained using this hybrid architecture of WPD and ANN.