The smart devices in Internet of Things (IoT) need more effective data storage opportunities, as well as support for Artificial Intelligence (AI) methods such as neural networks (NNs). This study presents a design of new associative memory in the form of impulsive Hopfield network based on leaky integrated-and-fire (LIF) RC oscillators with frequency control and hybrid analog–digital coding. Two variants of the network schemes have been developed, where spiking frequencies of oscillators are controlled either by supply currents or by variable resistances. The principle of operation of impulsive networks based on these schemes is presented and the recognition dynamics using simple two-dimensional images in gray gradation as an example is analyzed. A fast digital recognition method is proposed that uses the thresholds of zero crossing of output voltages of neurons. The time scale of this method is compared with the execution time of some network algorithms on IoT devices for moderate data amounts. The proposed Hopfield algorithm uses rate coding to expand the capabilities of neuromorphic engineering, including the design of new hardware circuits of IoT.