  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.
