This paper addresses the problem of performing time series analysis on-board a spacecraft, where the number of constraints is much bigger than for applications running in regular (i.e., ground-based) environments. An objective of modern spacecraft technologies designed for space exploration is to perform on-board data processing tasks, in order to increase the amount of data available for scientific analysis. Field Programmable Gate Array (FPGA) devices are considered as good candidates for hardware implementations of such systems. In order to optimize the usage of on-board resources, FPGAs share their resources between several digital signal processing (DSP) algorithms. In this paper, we describe the design and implementation of such an optimized design where two DSP algorithms are implemented on the same FPGA: (1) the power spectral density and (2) the multiscale probability distribution functions. The entire implementation process is described in detail, including a discussion about the main architectural choices. The proposed solutions focus on optimization of area, speed, and power. The tests performed, on both synthetic and real data, demonstrate the feasibility of our approach and constitute the first step toward porting the design on space-grade FPGAs.