Page 326 - Fundamentals of Radar Signal Processing

be the magnitude of the matched filter output waveform at t = t compared
max
to the value at t when there is no Doppler shift? Which of these
max
waveforms is most Doppler tolerant in this case? Which is least Doppler
tolerant?

_____________
1
This phase shift term was absorbed into the effective reflectivity ρ′ in Chap. 2.
2
Note that a frequency component of 1/τ hertz goes through exactly one full cycle during a pulse of
duration τ seconds.
3 2
Some authors define the term “ambiguity function” as | Â(t, F )| or as Â(t, F ) itself. Also, some authors
D
D
define the ambiguity function as .
The definition used here is consistent with that given in Rihaczek (1996).
4
A slightly more complicated version of this result holds when T ≤ 2τ, see (Levanon and Mozeson, 2004).
5 Group delay in seconds is the negative of the derivative of the frequency-domain phase function Φ(Ω) of

H(Ω) = | H(Ω) | exp[jΦ(Ω)] with respect to Ω. It is a measure of the filter delay for inputs of a given
frequency. See Oppenheim and Schafer (2010).
6
The lower case w is used for the frequency-domain window function w(F) to emphasize that the
multiplying function is the window function itself (e.g., a Hamming window) rather than its Fourier
transform.
7
Array antennas can also be steered using time delay units at each element or a combination of phase
steering within a subarray and time delay steering across subarrays. Pure time-delay-steered arrays do not
suffer antenna steering errors due to wideband waveforms.
8
While “fine” is preferred in this text to “high” to describe small values of resolution, the term “high range
resolution profile” is well-established in the literature.
9
This figure may appear to violate the earlier claim that the continuous autocorrelation function is a linear
interpolation between the discrete autocorrelation values of the code sequence exp(jϕ ). However, linear
n
interpolation of the complex values does not result in linear interpolation of the magnitude; see Prob. 4.24.