Time-Frequency Analysis of Radar Range Profiles - Time-Frequency Transforms for Radar Imaging and Signal Analysis - page 76

Figure 4.7 Joint time-frequency image of the back-scattering data from a slotted wave-

guide structure. The data were simulated using a method of moments solver.
The joint time-frequency image is generated by the STFT. The joint time-
frequency image shows both the early-time discrete-time returns from the slot
exterior and the late-time dispersive mechanisms due to modal propagation
inside the waveguide. ( Source: [17] Ó 1995 IEEE.)

energy is coupled into the waveguide, propagating to the other end as a sum
of waveguide modes. The energy carried by these modes begins to reradiate
through the other slot after a time given by L / c , where L is the length
between the two slots. However, this is the time delay only for frequencies
well above the modal cutoff, for which the modal group velocity approaches
c . For frequencies approaching the cutoff frequency of the respective mode,
the group velocity tends to zero and the time delay goes to infinity. Conse-
quently, each modal dispersion behavior is manifested as a time-frequency
trajectory with negative slope, as illustrated earlier in Figure 4.3(d). This
behavior can be clearly identified in the spectrogram, where the presence of
two modal dispersion curves with cutoffs at 3 GHz and at 6 GHz are
observed. They correspond to the TE 10 and TE 20 mode in the waveguide.
Note that the amplitude variation of the signal along these curves is governed
by the coupling mechanisms through the slot apertures and is considerably
more complex. Since multiple reflections occur, we also see other dispersion
curves with greater delays during the late-time portions of the return. The
first one corresponds with the energy that, upon reaching the other end,
reflects back and radiates through the slot on the left. The next is the three-
bounce mechanism. Note that energy is also coupled into the waveguide
through the slot on the right, and through similar mechanisms generate
dispersion curves in the time-frequency plot depending on the number of
bounces.