Review of Analog Signal Processing Basics - Digital Signal Processing: Fundamentals and Applications - page 783

Table B.1 Fourier Series Expansions for Some Common Waveform Signals in the
Sine-Cosine Form
Time Domain Signal xðtÞ Fourier Series Expansion

sin

x t ¼ 2 þ

2 A

p

1
3 sin 3

1
5 sin 5

1
7 sin 7

u 0 t þ u 0 t þ u 0 t þ u 0 t þ /

cos

x t ¼

4 A
p

1
3 cos 3

1
5 cos 5

1
7 cos 7

u 0 t u 0 t þ u 0 t u 0 t þ /

cos

x t ¼

8 A

p

1
9 cos 3

1
25 cos 5

1
49 cos 7

u t þ u t þ u t þ u t þ / 0 0 0 0

2

sin u 0 t

x t ¼

2 A

p

1
2 sin 2u 0 t þ

1
3 sin 3u 0 t

1
4 sin 4u 0 t þ /

sin cos

x t ¼ Ad þ

pd
pd

2 Ad u t 0

sin 2 pd
2

cos 2 sin 3 pd

3

cos 3

þ 2 Ad u 0 t þ 2 Ad u 0 t þ /

pd pd

x t ¼

1
T 0 þ

2
T 0 ð

cos u 0 t þ cos 2 u 0 t þ cos 3 u 0 t þ cos 4 u 0 t þ / Þ