T0T2Tcf2t1tT20T2Tdf3t1tf4t
解：1
a0124
2
fT2T2T2a
22tcos
Ωtdt42tsi
Ωt24si
ΩtdtT0T
ΩTT
Ω00

4cos
π1212cos
π1
2T2Ω2
π
T2T2T2b
22tsi
Ωtdt42tcos
Ωt24cos
ΩtdtT0T
Ω0T
Ω0T
2cos
π01cos
π2
π
πf1t1cos
π21cos
Ωtcos
πsi
Ωt4
1
π
1
π2f2tf1tT11cos2
πcos
Ωtcos
πsi
Ωt24
1
π
1
π3f3tf2t11cos2
πcos
Ωtcos
πsi
Ωt4
1
π
1
π4f4tf2tf3t121cos2
πcos
Ωt2
1
π
36试将图示周期方波信号ft展开为傅立叶级数，画出其单边和双边振幅频谱图和相ft位频谱图，并求该信号的占有频带B1t解：方法一按定义计算310235
2j2
πtj4
πj2
πjjF02F
1e3dte31e313302
π2
π
πj
π
πjj
πj
πjj3ee3e31si
πe31Sa
πe32
π
π333

方法二利用微分性质，通过右图计算，并注意到23
j
1T2j
ΩF
1t1tej
Ωtdte31TT2j2
πjjj
3πj
3πj
3πF
e31eee12
π2
π2
ft11011123t
jj1si
πe31Sa
πe3
π333作频谱如下

π

π
3
F02F10276120F2013860F30F400691203F5005560F60F10276120F2013860F30F40069120F5005560F60
P33
f单边频谱A
0670550280
24233
双边频谱
F

06702802800701401400700550055014011
4


24202423333
4



0
3232483323
4


4
2
2332483323
4
323
0


由图易知：B2（注意：2）37A…0T2Ta试求题图37所示周期信号的指数型傅里叶级数系数F
，并画出其幅度频谱。f1t…tA…0T2Tbf2t…tf3tA…0t0cA…t0TtAd0f4tT2Tt
j
1Ωtj
1ΩtT2T2e解：aF
1AejΩtejΩtej
ΩtdtAeT0j22T
1Ω
1Ω0
T
A
02462A
偶数π1
22F
bF
π1
r