Modern radio astronomy’s demand for high sensitivity and wide fields of view is met through innovations that reduce receiver system noise temperatures and integrate technology supporting parallel processing and larger instantaneous bandwidths. The advanced L-band phased array camera for astronomy (ALPACA) is a fully cryogenic 69 dual-polarized dipole PAF and digital beamformer back end for the Green Bank Telescope. This instrument will form 40 dual-polarized beams yielding a 0.35 sq. deg field of view on the sky with a 305.2 MHz processing bandwidth. The target system noise temperature is 27 K. A structured technique to map critically sampled and oversampled polyphase filter banks (PFBs) onto a systolic array for implementation on a field programmable gate array (FPGA) is shown. This method provides unique insights into the operation of these algorithms. A case study for an oversampled PFB operating at 666.67 Msps shows that these designs effectively utilize FPGA resources, maintain high-throughput, and are flexible solutions for varied application requirements. A new class of FPGA, the Radio Frequency System-on-Chip (RFSoC), is integrated as a full-functioning software-defined hardware platform in an open-source signal processing toolchain. This provides astronomers with essential hardware for contemporary scientific research. The demonstration for an experimental technique for measuring antenna radiation efficiency using the antenna Y factor method is presented. The noise contribution of the ALPACA dipole when operating at cryogenic temperatures is estimated. Our findings show that the antenna is expected to contribute less than 1 K to the instrument’s overall system noise temperature. Research contributions of this work are: the integration of new high-performance digital hardware in radio astronomical PAF digital back ends, an open-source RFSoC signal processing development toolchain, an oversampled PFB using an FPAG-based systolic array design, and estimating the cryogenic noise temperature of an ALPACA dipole from its radiation efficiency.