The growing demands for delivering multimedia services over Internet and wireless networks call for high-performance and low-complexity data compression and transmission algorithms. Various such algorithms are developed in this dissertation using the filter bank theory. We, first present a systematic design of multiplierless approximation of the Discrete Cosine Transform (DCT). Our method simplifies both software and hardware implementations and enables lossless compression. A family of fast lapped transforms is presented next, which employs time-domain pre- and post-processing of the DCT. These low-complexity algorithms enable DCT-based image, compression schemes to achieve performances comparable to that of the JPEG2000, the next-generation image compression standard. With the insights gained front the new lapped transform, several generalizations are developed. First, we propose a general structure for linear-phase paraunitary filter banks that employs multiple stages of pre- and post-processing of the DCT. This structure allows all DCT-based filter banks to be analyzed under one unifying umbrella. It also provides flexible trade-offs between complexity and performance by the joint design of pre- and post-processing. Secondly, we design the optimal pre- and post-processing for wavelet-based image and video compression. We then generalize the pre/post-processing scheme to oversampled filter banks, and introduce and efficient structure for oversampled linear-phase filter banks. Finally, the application of oversampled/redundant filter bank in channel equalization is investigated, and a modified Orthogonal Frequency Division Multiplexing (OFDM) scheme is proposed, which inherits the simplicity of OFDM as well as the performance of eigen-decomposition-based filter bank precoding method.