The authors propose and demonstrate the time-stretched short-time Fourier transform (TS-STFT) technique to overcome the limitation of an analog-digital converter (ADC) in the time-frequency analysis of ultrafast signals. Experimentally, the time-frequency analysis of highly chirped RF signals, with a chirp rate as high as 350 GHz/ns, is demonstrated. An effective real-time sampling rate of 320 GSa/s is achieved. Time stretching enhances the analog bandwidth and the effective sampling rate of the ADC and enables measurement of the instantaneous behavior of highly nonstationary ultrawideband signals.