Review of Analog Signal Processing Basics - Digital Signal Processing: Fundamentals and Applications - page 789

Table B.3 Fourier Transforms for Some Common Signals
Time Domain Signal xðtÞ Fourier Spectrum XðfÞ

X f ¼ A s

sin pf s

pf s

sin 2

X f ¼ A s

pf s
pf s

cos

X f ¼

2 A s

p

pf s
1 4f

2 2

s

sin

e jpf s 1 X f ¼

j 2 pf s

pf s

pf

X f ¼

A
a þ j

2 pf

XðfÞ¼A

Z N

d t s e jut dt ¼ e jut t¼ s ¼ e ju s

X u ¼

N

Example B.8 shows how to use the table information to determine the Fourier transform of a nonperiodic signal.