This paper presents a novel signal processing implementation for a dielectric materials characterization method using the hardware/software co-design methodology for application acceleration and rapid deployment on heterogeneous embedded platforms. The dielectric materials characterization method uses Frequency Modulated Continuous Wave radar systems for measurement purposes. Since the dielectric materials characterization method is intended to be used in a mobile materials characterization setup. The required signal processing algorithm of the materials characterization method is implemented on a Xilinx Zynq Ultrascale+ Multiprocessor System-on-Chip. Whereas, the intensive computing part of the algorithm is implemented on the hardware partition using high level synthesis design methodology for purposes of acceleration. The remaining parts of the algorithm are executed in software on the processing system part of the multiprocessor system on chip platform. The execution time, hardware resources utilization and energy consumption of the proposed co-design are determined experimentally. Furthermore, several optimization techniques are explored in order to reduce the total energy consumption and increase the data transfer bandwidth between the hardware and software partitions. The experimental results show a maximum speed up of 7.25 for the proposed co-design over the software reference model with an energy consumption less than 10 Joule.