Time-frequency transform based on frequency-to-time mapping and filtering

In this work, time-frequency transform systems reported recently by us, including short-time Fourier transform and wavelet-like transform, are introduced. A periodic fast frequency-sweep electrical signal is used to scan the signal under test (SUT). As long as the sweep is fast enough, the SUT in a single sweep period can be seen as a stationary signal and its frequency in this period can be obtained by mapping it to low-frequency pulses using filtering and frequency-to-time-mapping technique. After obtaining the frequency information of the SUT in each sweep period, the time-frequency information of the SUT can be obtained by combining the frequency information in each sweep period. The proposed method converts the time-frequency analysis of broadband signals into the analysis of low-speed electrical pulses, greatly increasing the real-time performance of the system and not relying on dispersive mediums compared to existing photonics-assisted solutions. The method for improving the system performance is also discussed by introducing filter bandwidth manipulation technology. It is found that for a given sweep speed, a proper filter bandwidth can be found to minimize the width of the electrical pulses and optimize the system frequency resolution. The photonics-assisted analog time-frequency transform method introduced in this work has a broad application prospect in the efficient and real-time acquisition of two-dimensional time-frequency information of the electromagnetic spectrum.