  A photonics-enabled wavelet-like transform system, characterized by
multi-resolution time-frequency analysis, is proposed based on a typical
stimulated Brillouin scattering (SBS) pump-probe setup using an optical
nonlinear frequency-sweep signal. In the pump path, a continuous-wave optical
signal is injected into an SBS medium to generate an SBS gain. In the probe
path, a periodic nonlinear frequency-sweep optical signal with a time-varying
chirp rate is generated, which is then modulated at a Mach-Zehnder modulator
(MZM) by the electrical signal under test (SUT). The optical signal from the
MZM is selectively amplified by the SBS gain and converted back to the
electrical domain using a low-speed photodetector, implementing the periodic
SBS-based frequency-to-time mapping (FTTM). The frequency-domain information
corresponding to different periods is mapped to the time domain via the FTTM in
the form of low-speed electrical pulses, which is then spliced to analyze the
time-frequency relationship of the SUT in real-time. The time-varying chirp
rate in each sweep period makes the signals with different frequencies have
different frequency resolutions in the FTTM process, which is very similar to
the characteristics of the wavelet transform, so we call it wavelet-like
transform. An experiment is carried out. Multi-resolution time-frequency
analysis of a variety of RF signals is carried out in a 4-GHz bandwidth limited
only by the equipment.
