數字信號處理—基于計算機的方法第4章答案

jω t

c

4-1 Show that if υ(t) = Re{g(t)e } , Eqs. (4-1b) and (4-1c)

θ

j (t)

are correct, where g(t) = x(t)+jy(t)=R(t)e .

Solution:

jω t jθ(t) jω t

υ(t) = Re{g(t)e c }= Re{R(t)e e c }

j[ω t+θ(t)]

υ(t) = Re{R(t)e c }= R(t) cos[ω t+θ(t)]

c

jω t

or. υ(t) = Re [ x(t) + jy(t)]e c

{ }

= Re [x(t) + jy(t)][cosω t+ jsin ω t]

{ c c }

= Re{x(t) cosω t+ jx(t) sin ω t+ jy(t) cos ω t? y(t) sin ω t}

c c c c

υ(t) = x(t) cosω t? y(t) sinω t

c c

4-2 A double-sideband suppressed carrier (DSB-SC) signal s(t)

with a carrier frequency of 3.8 MHz has a complex envelope

g(t)=Am(t). A=50V, and the modulation is a 1-kHz sinusoidal

c c

test tone described by m(t)=2sin(2 π 1,000t) , Evaluate the

voltage spectrum for this DSB-SC signal.

Solution:

using (2-26) with the help of Sec. A-5

δ δ

G(f)=AcM(f)=50[-j (f-1000)+j (f+1000)]

Substituting this into (4-15) and using δ(-f)=δ(f)

the voltage spectrum of this DSB-SC signal is

δ δ

S(f)=-j25 (f-f -1000)+j25 (f-f +1000)

c c

δ δ

-j25 (f+f -1000)+j25 (f+f +1000)

c c

4-3 Assume that the DSB-SC

總結

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