Processing sensor data with spiking neural networks on digital neuromorphic chips requires converting continuous analog signals into spike pulses. Two strategies are promising for achieving low energy consumption and fast processing speeds in end-to-end neuromorphic applications. First, to directly encode analog signals to spikes to bypass the need for an analog-to-digital converter (ADC). Second, to use temporal encoding techniques to maximize the spike sparsity, which is a crucial parameter for fast and efficient neuromorphic processing. In this work, we propose an adaptive control of the refractory period of the leaky integrate-and-fire (LIF) neuron model for encoding continuous analog signals into a train of time-coded spikes. The LIF-based encoder generates phase-encoded spikes that are compatible with digital hardware. We implemented the neuron model on a physical circuit and tested it with different electric signals. A digital neuromorphic chip processed the generated spike trains and computed the signal's frequency spectrum using a spiking version of the Fourier transform. We tested the prototype circuit on electric signals up to 1 KHz. Thus, we provide an end-to-end neuromorphic application that generates the frequency spectrum of an electric signal without the need for an ADC or a digital signal processing algorithm.