Page 149 - Fundamentals of Radar Signal Processing

(2.89)

so that (Gleiser, 1979; DiFranco and Rubin, 2004; Peebles, 1998)

(2.90)

If the transmitted waveform is a standard RF pulse

(2.91)

where A(t) is the pulse envelope, the received echo waveform will be

(2.92)

Inspection of Eq. (2.92) reveals several characteristics of the received

signal. Its frequency is α F Hz. The change in frequency is the Doppler shift
t
v
F :
D

(2.93)

The Doppler shift is positive for approaching targets (v > 0) and negative for
receding targets as expected. The phase of the received signal is decreased by

(2.94)

The waveform is scaled in time by the factor α . For example, for an
v
approaching target, α > 1 and a transmitted pulse is shortened by a factor of α v
v