Recent developments in the field of phased array feeds for radio astronomical reflector antennas, have opened a new frontier for array signal processing for radio astronomy observations. The goal is to replace single horn feeds with a phased array feed, so as to enable astronomers to cover more sky area in less time. The development of digital backend signal processing systems has been a major area of concentration for the development of science-ready phased array feeds for radio astronomers. This thesis focuses on the development of analog down-converter receivers and an FPGA-based digital backend for real-time data processing and analysis support for phased array feeds. Experiments were conducted with new receiver boards and both single-polarization and dual-polarization phased array feeds at the Arecibo Observatory, Puerto Rico and at the 20-meter telescope at Green Bank, WV, and results were analyzed. The experiments were performed as a part of a feasibility study for phased array feeds. The new receiver boards were developed as an upgrade to the earlier connectorized receivers as the number of input channels increased from 19 to 38 and space constraints arose due to the large size of the earlier receivers. Each receiver card has four independent channels on it. The receiver cards were found to have lower cross-coupling between the channels in comparison to the earlier receivers. The development of a FPGA-based real time digital backend focused on a real-time spectrometer, beamformer and a correlator for all the 64-channels using a x64 ADC card and ROACH FPGA boards. The backend can plot results in real time and can stream and store the data on the computers for purpose of post-processing and data analysis. The design process uses libraries and blocks provided by the Center for Astronomy Signal Processing and Electronics Research (CASPER) community.