Fig. 4: Demonstration of user-defined direct synthesis of the wave joint TF distribution.

The experimental setup is shown on the left and the results are captured from the real-time oscilloscope. a Measured temporal waveform of the SUT, which is composed of periodic sinc-like pulses, forming a nearly uniform spectrogram distribution, over a frequency range up to 23 GHz (positive side) along a duration of ∼ 300 ns. The frequency roll-off shown in the numerical STFT shows a good agreement with the measured frequency spectrum of the input pulse train (see Fig. 7 in the Supplementary file). b 1D temporal filtering mask mapped from the 2D image of the Mona Lisa painting used to manipulate the TF distribution of the SUT, and a zoom of the user-defined temporal filtering pattern of arbitrary shape. c The 2D representation of the TM-SP trace that is measured after the temporal filtering shows that the synthesised spectrogram closely follows the contour of the target image. d Using the same SUT as in (a), the filtering mask is now designed to craft a joint TF distribution resembling the Chinese character shown at the top left, which is achieved by changing the passband width and centre location of the implemented temporal filtering. The short pulses at the edge of each time window are purposedly introduced to facilitate the synchronisation between the filtering mask and TM-SP. e The 2D representation of the TM-SP trace that is measured after the temporal filtering confirms that the synthesised spectrogram closely resembles the target character. The frequency roll-off in the synthesised spectrogram is consistent with that of the input sinc-like pulses (see Fig. 8 in the Supplementary file). SUT: Signal Under Test, STFT: Short-time Fourier Transform, TM-SP: Time-Mapped Spectrogram, 2D: two-dimensional, CW: Continuous-Wave laser, MZM: electro-optic Mach-Zehnder Modulator, PM: electro-optic Phase Modulator, LCFBG: Linearly Chirped Fibre Bragg Grating.