We present a novel method to determine the resonant frequency and quality factor of microwave resonators which is faster, more stable, and conceptually simpler than the yet existing techniques. The microwave resonator is irradiated at a frequency away from its resonance. It then emits an exponentially decaying radiation at its eigen-frequency when the excitation is rapidly switched off. The emission is down-converted with a microwave mixer, digitized and its Fourier transformation (FT) directly yields the resonance curve in a single shot. Being an FT based method, this technique possesses the Fellgett (multiplex) and Connes (accuracy) advantages and it conceptually mimics that of pulsed nuclear magnetic resonance. We also establish a novel benchmark to compare accuracy of the different approaches of microwave resonator measurements. This shows that the present method have similar accuracy to the existing ones.