Exact(4)
T a is the synthetic aperture time, f c is the carrier frequency, K r is the range FM rate, and c represents the speed of light.
where rect is the fast-time envelope, T r represents the pulse duration time, τ is the fast time variable, K r is the FM rate, and f r is the carrier frequency.
Inspecting (34), the first-order expansion is adopted to approximate the Doppler FM rate, and this will cause an inevitable error along azimuth direction which is called the quadratic phase error (QPE).
Bats control many aspects of their echolocation calls such as signal duration, rate and direction of frequency modulation (FM), rate and magnitude of amplitude modulation (AM), signal bandwidth, harmonic structure, and both the number and timing of calls emitted (Gunderson, 1976; Fenton et al., 1987; Fenton et al., 2011).
Similar(56)
where K aA is the Doppler FM rate of the reference target A, and K s is the coefficient of azimuth-variant component of the Doppler FM rate.
To get the formation of the scaling function, one needs to know the range migration trajectory and the frequency modulation (FM) rate of the signal.
Here, we use the expression of Doppler FM rate for CTSSAR.
Inspecting (28), the Doppler FM rate is determined by the slant range at the beam center crossing time, r Rc.
In this subsection, the QPEs along azimuth direction based on the expressions of Doppler FM rate in (34), [20, 21] are analyzed, respectively.
A linear transform with a kernel that matches these phase functions maps these signals to impulses in the FM rate domain.
The Doppler FM rate K a can be expressed as {K}_a=-frac{B_0{f}_c}{c}=-frac{v^2{ cos}{lambda{rheta}_{mathrm{Rc}mbda {r}_{mathrm{Rc}}}.
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