One of the key trends in the design of radio receivers and other wireless devices is to shift more and more of the transceiver functionalities to digital signal processing (DSP). At the same time, the demands on the remaining analog circuits are greatly increased, especially with lower power supplies and nanoscale technology effects such as variability. With the terminal users requesting high radio performance and data rates, and low power consumption on one hand, and terminal flexibility and reduced implementation costs on the other hand, the requirements for these remaining analog front-end stages become extremely challenging to meet. As a result, one interesting idea is to complement analog radio-frequency (RF) circuits with smart signal-processing algorithms to digitally enhanced RF circuits. In this paper, we focus on developing and demonstrating novel signal-processing techniques intended for the analog and digital front-ends of future low-power, flexible radios. One key aspect in the work is power-efficient digital front-end design with great flexibility for digital selectivity filtering and sample rate alteration. Another key ingredient is the analysis and mitigation of different analog RF impairments, with special emphasis on I/Q imbalance effects and second-order intermodulation (IM2) distortion in wideband multicarrier or multichannel radio receivers. The approach used in this work generally draws from the practical system performance specifications. Overall, our results clearly indicate that the proposed compensation techniques can be used to suppress I/Q imbalance and IM2 distortion effects in receiver front-end sections under realistic signaling assumptions. The adaptivity and flexibility offered by the overall digital front-end design greatly reduces the power consumption of the radio.