Redundant representations have traditionally been developed for image processing and have been typically too computationally demanding to be applied to modern day multi-channel signal processing problems, where one has to deal with very large quantity of data and an environment that changes much faster than what is usually encountered in image processing. In this work, we address two multi-channel signal processing problems, underdetermined blind source separation (BSS) of audio and signal time variability in brain machine interface (BMI) by developing sparse decomposition methods for learning signal representation from the data, and designing algorithms to exploit the resulting sparseness and redundancy. By exploiting sparseness in a redundant overcomplete representation, we develop algorithms that can efficiently separate mixtures of audio signals into their underlying sources. The applications of BSS range from denoising in pervasive devices such as cellular phones to digital re-mastering of old music recordings. In BMI, we learn subspaces where inherent features of multi-channel Local Field Potential (LFP) data are recurrent, and use projection onto those subspaces to improve movement direction classi cation across recording sessions.