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 pumped with the microwave radiation 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 emitted microwave signal is down-converted with a microwave mixer, digitized, and its Fourier transformation (FT) directly yields the resonance curve in a single shot. Being a 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 has similar accuracy to the existing ones, which are based on sweeping or modulating the frequency of the microwave radiation.
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