Fig. 1. Simulation setup of the real time Fourier transformation based on discrete dispersion

Fig. 2. Scheme to realize discrete dispersion based on cascaded optical ring resonators

Fig. 3. Simulated FTM based on discrete dispersion. (a) Periodic FTM output; (b) Zoom in one period, waveforms of different color correspond to different input frequencies; (c) FTM outputs under 0 (black line) and 50 MHz (blue line) frequency shift; (d) Calculated FTM of simulation (colorful dots) and theory prediction (black line)

Fig. 4. Two-dimensional analysis of joint time-frequency energy distribution of different input signals. (a) The input is a linear chirped signal; (b) The input is two linear chirped signals with opposite chirping rate; (c) The input is frequency hopping signal; (d) The input is a linear chirped signal together with random isolated interfering frequency transients