Page 223 - Fundamentals of Radar Signal Processing

bandwidth of the pulse spectrum, in Hz? What is the 3 dB bandwidth in

Hz?

4. Consider two signals: a square pulse x (t) of length τ seconds, and a
1
triangle x (t) of length 2τ seconds obtained by convolving the square pulse
2
with itself, x (t) = x (t) * x (t). What is the relationship between the two
1
1
2
spectra X (F) and X (F)? Determine the relationship between the 3-dB
2
1
bandwidths of X (F) and X (F). How does this compare to the relationship
1
2
between the Rayleigh bandwidths of X (F) and X (F)?
2
1
5. Consider two RF pulses at frequencies of 5.0 GHz and 5.01 GHz. Assume
two pulses are resolvable in frequency if their center frequencies are
separated by at least the Rayleigh resolution of the individual pulses. What
is the minimum pulse length required so that the two pulses could be
resolved in frequency?

6. A finite pulse train waveform is composed of 20 pulses, each of 10 μs
length and separated by a PRI of 1 ms. What is the coherent processing
interval for this waveform?

7. Consider an X-band (10 GHz) radar on a aircraft traveling at 100 m/s.
Assume the 3-dB azimuth beamwidth of the antenna is 3°. Compute the
Doppler shift F of a scatterer on the antenna boresight and the Doppler
D
bandwidth β across the beam for squint angles of ψ = 0°, 30°, 60°, and
D
90°.

8. Consider a radar with a PRF of 5 kHz. What is the maximum unambiguous
range, R , of this radar in km? If a target is located at a range of 50 miles,
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how many pulses will the radar have transmitted before the first echo from
the target arrives? What will be the apparent range of the target in
kilometers?

9. Assuming a sidelooking radar (ψ = 90°) and Nyquist sampling in slow
time, determine the relationship between the maximum unambiguous range
R and the antenna beamwidth θ . Ignore eclipsing. Using θ ≈ λ/D ,
az
ax
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ax
determine the relationship between R and the antenna azimuth dimension
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D .
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10. Suppose a target is at a range of 10 km from a C-band (5 GHz) radar and
has a radial velocity of +50 m/s with respect to the radar. Determine
whether the target is ambiguous in range and velocity, and the apparent
range and velocity R and v for PRFs of 1, 10, and 100 kHz. The
a
a
unambiguous velocity interval is considered to be [–v /2, +v /2].
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11. Suppose a C-band (5 GHz) radar has a fast-time sampling rate of 2M
samples per second and a PRF of 5000 pulses per second. A CPI of data is
to be collected that will cover a range interval of 30 km and support
velocity resolution of 10 m/s. What are the dimensions of the data matrix