After several decades of continuously optimizing computing systems, the Moore's law is reaching its end. However, there is an increasing demand for fast and efficient processing systems that can handle large streams of data while decreasing system footprints. Neuromorphic computing answers this need by creating decentralized architectures that communicate with binary events over time. Despite its rapid growth in the last few years, novel algorithms are needed that can leverage the potential of this emerging computing paradigm and can stimulate the design of advanced neuromorphic chips. In this work, we propose a time-based spiking neural network that is mathematically equivalent to the Fourier transform. We implemented the network in the neuromorphic chip Loihi and conducted experiments on five different real scenarios with an automotive frequency modulated continuous wave radar. Experimental results validate the algorithm, and we hope they prompt the design of ad hoc neuromorphic chips that can improve the efficiency of state-of-the-art digital signal processors and encourage research on neuromorphic computing for signal processing.