Page 339 - Fundamentals of Radar Signal Processing

(5.1)

It is common to work with normalized frequency f = FT cycles per sample
or with the radian equivalent, ω = ΩT = 2πFT radians per sample. In terms of
normalized radian frequency the frequency response of the two-pulse canceller
is

(5.2)

Recall that as F ranges from –1/2T to +1/2T, f ranges from –0.5 to + 0.5 and ω

from –π to +π.
Figure 5.9a plots the magnitude of the frequency response of the two-pulse
canceller. The filter does indeed have a null at zero frequency to suppress the
clutter energy. Spectral components representing moving targets may either be
partially attenuated or amplified, depending on their location on the Doppler
frequency axis. As with all discrete-time filters, the frequency response is

periodic with a period of 1 in the normalized cyclical frequency variable f,
corresponding to a period of 2π in the normalized frequency variable ω or a
period of 1/T = PRF in actual frequency in hertz. The shaded area highlights the
principal period from –PRF/2 to +PRF/2; this is all that is normally plotted.
Considering only this frequency range, it is clear that the frequency response is
highpass in nature. The implications of the periodicity will be considered in
Sec. 5.2.4.