Page 87 - Fundamentals of Radar Signal Processing

15. What is the Nyquist sampling rate (minimum rate to avoid aliasing) for the

signal x(t) having the spectrum X(F) shown in the figure below? Sketch a
block diagram of a system for recovering a new signal from samples of
x(t) taken at the Nyquist rate, such that the spectrum has the same shape
as X(F), but is centered at F = 0.

16. In some cases, the spectrum replication property of sampling can be used as

a substitute for demodulation. Given a signal x (t) with the spectrum
a
shown, what is the lowest sampling rate that will ensure both no aliasing of
the spectrum, and that one of the spectrum replicas is centered at F = 0?

17. How many bits are required in an A/D converter to provide a dynamic

range of at least 40 dB? What is the expected SQNR with this number of
bits, assuming k = 3?

18. Numerical values of spatial frequency differ greatly from the usual temporal
frequency values. What is the spatial frequency in cycles per meter for a 1-
GHz electromagnetic wave?

19. What is the instantaneous frequency in hertz of the waveform x(t) = exp[j ·
exp(–αt)]?

20. Determine a phase function ψ(t) such that the instantaneous frequency in
hertz of the waveform x(t) = cos[ ψ(t)], –τ/2 ≤ t ≤ τ/2 seconds, sweeps
linearly from –β/2 Hz to +β/2 Hz.

21. Suppose signal x is 30 dB greater in power than signal x . What is the ratio
1
2
of their power in linear units (i.e., not in dB)? What is the ratio of the
corresponding voltages?

_____________