It is demonstrated experimentally that a spin-torque nano-oscillator (STNO) rapidly sweep-tuned by a bias voltage can be used for time-resolved spectrum analysis of frequency-manipulated microwave signals with complicated multi-tone spectra. The critical reduction in the time of spectrum analysis comes from the naturally small time constants of a nano-sized STNO (1-100 ns). The demonstration is performed on a vortex-state STNO generating in a frequency range around 300 MHz, with frequency down-conversion and matched filtering used for signal processing. It is shown that this STNO-based spectrum analyzer can perform analysis of multi-tone signals, and signals with rapidly changing frequency components with time resolution on a $mu$s time scale and frequency resolution limited only by the bandwidth theorem. The proposed concept of rapid time-resolved spectrum analysis can be implemented with any type of micro and nano-scale frequency-swept oscillators having low time constants and high oscillation frequency.
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