Throughput, spectral efficiency and power consumption are the three major factors that drive the evolution of the communication systems. The data rate of modern wireless communication has increased from 10 kb/s (1995 narrow band GSM) to over 100 Mb/s (2015 LTE Advanced) in just twenty years. The data rate of the wired communication has reached more than 2 Gb/s to accommodate the fast growing cellular data rates. The Moore's law is still in effect and the wideband communication era continues to become more entrenched in our daily lives! Dealing with wideband signals poses great challenges to our existing signal processing approaches. At a high sample rate, i.e., GHz level, any non-trivial signal processing, e.g., digital filtering, may saturate the processing resources. This is because the signal's sample rate has become comparable to the hardware's clock rate! At such high rate, significant amount of hardware resources or parallelism is needed to execute the required number of multiply and accumulation operations. This phenomenon is the bottleneck in our further pursuit of higher data rate communication and will raise the hardware cost significantly. This dissertation tackles several challenging wideband signal processing problems in communication system design. In particular, we propose the non-maximally decimated filter bank (NMDFB) based digital filtering approach. A key attribute of this structure is that the filtering is achieved via the intermediated processing element (IPE) embedded in between a pair of analysis and synthesis NMDFB. The polyphase implementation of NMDFB has its workload on the same order as the FFT and is thus extremely efficient. This type of digital filter implementation not only allows the signal processing to be performed at a significantly reduced sampling rate but also exhibits significant savings in power consumption over the conventional approaches. The NMDFB based processing supports many if not all of the commonly used filtering tasks in communications, and therefore can be used to implement a wideband receiver. We demonstrate this by developing a NMDFB based efficient linear / non-linear equalization techniques for single carrier QAM signal. We also address the carrier and symbol timing synchronization problems based on NMDFB approach. Besides the filtering tasks, the NMDFB based architecture also enables several key signal processing tasks required by the future's communication systems. We show NMDFB can be used as the basis of an efficient wideband diversity combiner over frequency selective channels. We also demonstrate advanced channelization technique based on NMDFB. Unlike the existing channelizers that often pose constrains on either signal format or signal spectrum, the proposed channelizer is able to channelize multiple signals with arbitrary center frequency, arbitrary bandwidth and arbitrary format.