Page 60 - Fundamentals of Radar Signal Processing

Part (a) of the figure shows a portion of the positive frequency spectrum of the

sum of two unit amplitude cosine functions with zero initial phase, one at 1000
Hz and one at 1500 Hz. This signal could represent the Doppler spectrum of two
moving targets with the same echo strength but different radial velocities. The
observation time is such that the mainlobe of the sinc function contributed by
each has a Rayleigh width (peak to first null width) of 100 Hz. The two vertical
dotted lines mark the two cosine frequencies. There are two distinct, well-

separated peaks in the spectrum. The actual frequency of each peak is perturbed
very slightly from the expected value by the sidelobes of the other sinusoid.
Nonetheless, these two signal components are considered well resolved. Parts
(b) through (d) of the figure repeat this measurement with the frequency spacing
reduced to 100, 75, and 50 Hz. At 100 Hz spacing the two spectral peaks are
still well resolved, though with more perturbation of the apparent frequencies,
but as the separation drops below the Rayleigh width to 75 and then to 50 Hz,

they blur into a single spectral peak. At 50 Hz, they are no longer resolved; the
spectrum measurement does not show two separate signals. At 75 Hz they are
marginally resolved, although a little noise added to the data would make that a
precarious claim. It appears that a separation of about the Rayleigh width or
greater is needed for clear resolution of the two frequencies. This demonstration
also suggests that the width of the signature of a single isolated target is the

major determinant of the system’s resolution.