This work proposes a digital implementation of an Oscillatory Neural Network (ONN) in a Field-Programmable Gate Array (FPGA), demonstrating excellent associative memory capabilities. This work goes beyond previous implementations by enabling on-chip learning directly in the FPGA. More specifically, we implement on-chip Hebbian learning, and we compare three different design strategies. The first strategy takes advantage of a System-on-Chip (SoC) composed of a Processing System (PS) and Programmable Logic resources (PL) to integrate Hebbian learning in PS. The two other strategies implement the Hebbian learning directly in PL. We compare the three different design strategies on a digit recognition task in terms of accuracy, utilization, execution time, and maximum frequency. We show that implementing Hebbian learning in PL gives more advantages in terms of resource utilization and latency than implementing Hebbian in PS with several orders of magnitude because the weight matrix computation is performed in hardware. Moreover, we develop an application interface to demonstrate the pattern learning and recognition capabilities of our digital ONN implementation.