B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

504 RANDOM PROCESSES AND SPECTRAL ANALYSIS
(b) The shot noise in transistors can be modeled by
h(t) = :l._ e-t/T u(t)
T
where q is the charge on an electron and Tis the electron transit time. Determine and sketch
the autocorrelation function and the PSD of the transistor shot noise.
figure P.9.4-3
1-
9.6-1 A signal process m(t) is mixed with a channel noise n(t). The respective PSDs are
6
Sm (/) = 9 + (2rrj)2
and Sn(/) = 6
(a) Find the optimum Wiener-Hopf filter.
(b) Sketch its unit impulse response.
(c) Estimate the amount of delay necessary to make this filter closely realizable (causal).
(d) Compute the noise power at the input and the output of the filter.
9.6-2 Repeat Prob. 9.6-1 if
4
Sm(f) = 4 + (2:rr/)2
and
32
Sn (f) = 64 + (2:rr/)2
9.7-1 A message signal m(t) with
(ex = 3000rr)
DSB-SC modulates a carrier of 100 kHz. Assume an ideal channel with H c (f) = 10- 3 J and
the channel noise PSD Sn (f) = 2 x 10- 9 . The transmitted power is required to be I kW, and
G = 10-21.
(a) Determine transfer functions of optimum preemphasis and deemphasis filters.
(b) Determine the output signal power, the noise power, and the output SNR.
(c) Determine y at the demodulator input.
9.7-2 Repeat Prob. 9.7-1 for the SSB (USB) case.
9.7-3 It was shown in the text that when the baseband m(t) is band-limited with a uniform PSD,
PM and FM have identical performance from the SNR point of view. For such m(t), show that
optimum PDE filters in angle modulation can improve the output SNR by a factor of 4/3 (or 1.3
dB) only. Find the optimum PDE filter transfer functions.