Review of Analog Signal Processing Basics - Digital Signal Processing: Fundamentals and Applications - page 782

FIGURE B.6

Two-sided spectrum in Example B.3.

Similarly, applying Equation (B.19) leads to

lim
n / 0

¼ 2 j1j ¼ 2

jc 0 j ¼ 0:0002

sin ð n 2; 000p 0:0002=2Þ
ðn 2; 000p 0:0002=2Þ 0:001 10

sinð x Þ
x

Note: We use the fact that lim
x / 0

¼ 1:0 (see L'Hospital's rule in Appendix G).

¼ 2 ¼ 1:8710

j c 1 j ¼ j c 1 j ¼ 0:0002

sin ð1 2; 000p 0:0002=2Þ
ð1 2; 000p 0:0002=2Þ

sin ð0:2pÞ
0:2p 0:001 10

¼ 2 ¼ 1:5137

jc 2 j ¼ jc 2 j ¼ 0:0002

sin ð2 2; 000p 0:0002=2Þ
ð2 2; 000p 0:0002=2Þ

sin ð0:4pÞ
0:4p 0:001 10

¼ 2 ¼ 1:0091

jc 3 j¼jc 3 j¼ 0:0002

sin ð3 2; 000p 0:0002=2Þ
ð3 2; 000p 0:0002=2Þ

sin ð0:6pÞ
0:6p 0:001 10

¼ 2 ¼ 0:4677

jc 4 j ¼ jc 4 j ¼ 0:0002

sin ð4 2; 000p 0:0002=2Þ
ð4 2; 000p 0:0002=2Þ

sin ð0:8pÞ
0:8p 0:001 10

Figure B.6 shows the two-sided amplitude spectral plot.

The following example illustrates the use of table information to determine the Fourier series
expansion of the periodic waveform. Table B.1 consists of the Fourier series expansions for common
periodic signals in the sine-cosine form while Table B.2 shows the expansions in the complex
exponential form.