Time-Frequency-Based Radar Image Formation - Time-Frequency Transforms for Radar Imaging and Signal Analysis - page 110

Figure 5.6 (a) Image of a simulated MIG-25 reconstructed with the Fourier-based image

formation, and (b) image frame 7 reconstructed with the time-frequency-based
image formation.

without knowing the initial kinematic parameters and resampling the data,
a blurred Fourier image due to smeared Fourier spectrum will become a
sequence of clear range and instantaneous Doppler images.
In principle, any time-frequency transform can be used to replace the
Fourier transform for radar image formation. However, a desired time-
frequency transform should satisfy the following requirements: (1) it should
have high resolution in both the time and frequency domains, and (2) it
should accurately reflect the instantaneous frequencies of the analyzed signal.
As discussed in Chapter 2, time-frequency transforms include linear
transforms such as the STFT, and bilinear transforms such as the WVD.
The joint time-frequency resolution of the STFT is limited by the uncertainty
principle. With a time-limited window function, the resolution of the STFT
is determined by the window size. There is a trade-off between the time-
resolution and the frequency resolution. A larger window has higher fre-
quency resolution but lower time resolution; a smaller window has lower
frequency resolution but higher time resolution.
Unlike the STFT, in which the time and frequency resolution is deter-
mined by the selection of the short-time window function, there is no short-
time window involved in the WVD. The WVD not only has a higher
frequency resolution close to that of the full-size windowed Fourier transform,
but also provides a higher time resolution. Because of the high resolution
and the accuracy of the time-frequency representation, the WVD can be a
candidate for time-frequency-based image formation. However, there is cross-
term interference associated with the WVD. When the signal contains more
than one component, the WVD will generate cross-term interference between