A photonics-based short-time Fourier transform (STFT) system is proposed and experimentally demonstrated based on stimulated Brillouin scattering (SBS) without using high-frequency electronic devices and equipment. The wavelength of a distributed feedback laser diode is periodically swept by using a low-speed periodic sawtooth/triangular driving current. The periodic frequency-sweep optical signal is modulated by the signal under test (SUT) and then injected into a section of SBS medium. The optical signal from another laser diode as the pump wave is reversely injected into the SBS medium. After simply detecting the forward transmission optical signals in a low-speed photodetector, the STFT of the SUT can be implemented. The system is characterized by the absence of any high-frequency electronic devices or equipment. An experiment is performed. The STFT of a variety of RF signals is carried out in a 4-GHz bandwidth. The dynamic frequency resolution is demonstrated to be around 60 MHz.