0195136047.pdf

PROBLEMS 663

− 3

t

T/2 T

−T/2 T/4

−T/4

T/2

T/2

0

3

− 2

(a)

2

t

0

− 4

(b)

4

8

0 T t

(c)

6

− 6

Figure P14.1.15

10 kHz, withK=1, find and sketch the required

equalizer characteristics.

14.1.21The frequency response of a high-pass transmis-
sion system is given by
|H(f)|=
f/fco
1 +(f/fco)^2
;

θ(f)=90°−tan−^1 (f/fco)

withfco = ωco/ 2 π =100 Hz. Ifx(t)isa

triangular wave of Figure E14.1.4(b), withA=

π^2 /8 andT =25 ms, obtain an approximate

expression for the periodic steady-state response

y(t). See Figure 14.1.5.

14.2.1(a) Letx(t)=12 cos 2π 100 t+8 cos 2π 150 t,

andxc(t)=x(t) cos 2πfct, wherefc= 600

Hz. Sketch the amplitude spectrum.

(b) List all the frequencies in the productxc(t)

cos 2π 500 t, wherexc(t) is given in part (a).

14.2.2The input to the product modulator of Figure

14.2.1 is given byx(t)=8 cos 2π 3000 t+ 4

cos 2π 7000 t. The frequency of the carrier wave

is 6 kHz. Sketch the amplitude line spectrum of

the modulated wavexc(t).

*14.2.3Consider the following system withx(t)=12 cos

2 π 100 t+4 cos 2π 300 tand two ideal filters as

shown in Figure P14.2.3. Findxa(t) andxb(t).

14.2.4Consider the product modulator of Figure

14.2.4(a), where the oscillator generates

cos[2π(fc+f ) t+φ] in whichfandφare

synchronization errors. Findz(t) produced by the

following inputs, whenfm=1 kHz,f= 200

Hz, andφ=0:

(a) DSB inputxc(t)=4 cos 2πfmtcos 2πfct.

(b) Upper-sideband SSB inputxc(t)=2 cos

2 π(fc+fm)t.

(c) Lower-sideband SSB inputxc(t)=2 cos

2 π(fc−fm)t.