0195136047.pdf

664 SIGNAL PROCESSING

14.2.5Repeat Problem 14.2.4 whenfm=1 kHz,f=

0, andφ=90°.

14.2.6(a) Consider Figure 14.2.5, in which the signal

to be sampled isx(t)=18 cos 2π 20 t+ 12

cos 2π 60 t. Withfs=100 andD=Ts/2, for

0 ≤f ≤ 2 fs, sketch the amplitude line

spectrum ofxs(t).

(b) Then find the signaly(t) that would be re-

constructed by an ideal low-pass filter that

rejects allf>fs/2.

14.2.7(a) The continuous amplitude spectrum of the

input to a switching sampler (Figure 14.2.5)

is shown in Figure P14.2.7. For 0≤f≤

100, withfs=70 andD=Ts/4, sketch the

resulting spectrum ofxs(t).

(b) Suggest howx(t) can be reconstructed from

xs(t).

14.2.8PDM and PPM (see Figure 14.2.7) have the ad-

vantage of being immune to nonlinear distortion,

because the pulse is either on or off. However, in

exchange, the transmission bandwidth must be

B≥ 1 /D >> W, which is needed to accommo-

date pulses with durationD<<Ts≤ 1 /( 2 W).

LetDbe the pulse duration of the PPM waveform

in Figure 14.2.7. Let the maximum position shift

be±. For = 2 Dandfs=20 kHz, find the

maximum allowed value ofDand the minimum

required transmission bandwidth.

*14.2.9The TDM system of Figure 14.2.9 has a trans-
mission bandwidthB=250 kHz.

(a) Find the maximum number of voice signals

withW=4 kHz that can be multiplexed.

(b) Repeat part (a) with the additional constraint

that the TDM waveform be off for at least

50% of the time.

14.3.1An amplifier has a gain of 50 dB, a bandwidth

of 9 MHz, and a noise temperatureTa= 25 T 0 ,

whereT 0 is the room temperature, 290 K. Find

the output noise power and rms voltage across a

100-load resistor when the source temperature

T=T 0.

*14.3.2If the signal in Example 14.3.1 has a bandwidth of

600 kHz, determinePout/Noutassuming a noise-

less amplifier. Then check to see whether it is

possible to obtainPout/Nout≥ 105.

14.3.3A simpleRCfilter yields|H(ω)|^2 = 1 /[1+

(ω/ωco)^2 ], whereas a more sophisticated and rel-

atively more expensive Butterworth filter gives

|H(ω)|^2 = 1 /[1+(ω/ωco)^4 ]. Either of these

can be used to reduce the hum amplitude. Let

an information signal with significant frequency

content forf ≤30 Hz be contaminated by ac

hum at 120 Hz. The contaminated signal is then

applied to a low-pass filter to reduce the hum

amplitude by a factor ofα. For (i)α= 0 .25,

and (ii)α= 0 .1, determine the required cutoff

frequencyfcofor (a) theRCfilter, and (b) the

Butterworth filter, and suggest the filter to be used

in each case.

cos 2πfat = cos 2π 800 t

Ideal filter A

which rejects all

f < 800

Ideal filter B

which rejects all

f > 1200

x(t) xb(t)

cos 2πfbt = cos 2π 1200 t

Figure P14.2.3

Amplitude

0

20

f

40 60

Figure P14.2.7