1.4求符号函数（题图1-1a）和单位阶跃函数（题图1-1b）的频谱. 解:1) 符号函数的频谱:
令:
x1(t) lime
0
t
x(t);
X1(f) x1(t)e j2 ftdt
0 t t
j2 ft lim e( 1)edt ee j2 ftdt 0 0
1 j f
2)单位阶跃函数的频谱:
2
0
x(t) lime
t
x(t)
j2 ft
;
t1 j2 ft dt lim eedt 0 0 j2 f
22
-------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------- 1.5求被截断的余弦函数cosω0t（题图1-2）的傅立叶变换。
cos 0t;t T x(t)
t T 0;
解：
T
j2 ft X(f) x(t)edt cos2f0te j2 ftdt T
T1 j2 f0tj2 f0t j2 ft
e eedt
T2
sin(f f0)2Tsin(f f0)2T
T
(f f0)2T (f f0)2T
Tsinc 1 sinc 2
X(f) x(t)e
