
where the sinusoidal functions are the complex exponentials
e
jvt
¼ cos vt þ j sin vt (1 < v < 1)(4:296)
and the function F(jv) is given by
F(jv) ¼
ð
1
1
f (t)e
jvt
dt (4:297)
The complex-valued function F( jv) is called the Fourier integral or Fourier transform of the signal
f(t). Entire books have been written on the Fourier transform and its applications (Papoulis 1962;
Bracewell 1986) while other books in the area of signals and systems (Kailath 1980; Jackson 1991;
Kraniauskas 1992) include considerable coverage of the topic. F(jv) is a function that assumes
complex values over the frequency range (1, 1). In polar form, F( j v) is written as
F( jv)