1. The Average Normalized Power Spectrum and its Relevance (Examples 2
The Average Normalized Power Spectrum and its Relevance (Examples 2.9 and 2.10)

2. Example 2.9 – Draw the Power Spectral Density of a Rectangular Pulse Train
Rectangular Pulse Train (from Example 2.7):
volts 3 v ( t )
· · ·
· · ·
msec
-16
-14
-12
-10 -8
Time domain representation -6 -4 -2 2 4 6 8 10 12 14 16
Magnitude
in volts -2
-1.5 -1
-0.5
0.5 1
1.5 2
Frequency
in kHz
0.2
0.4
0.6
We’ve already determined the 2-sided magnitude spectrum (Ex. 2.7)

3. Converting 2-sided Magnitude Spectrum to 1-sided
in volts -2
-1.5 -1
-0.5
0.5 1
1.5 2
0.2
0.4
0.6
Frequency
in kHz
0.2
0.4
0.6
0.8 1
1.2
0.5
1.5 2
Magnitude
in volts
Frequency
in kHz

4. Determining Average Normalized Power Spectrum (squaring terms)
0.2
0.4
0.6
0.8 1
1.2
0.5
1.5 2
Magnitude
in volts
Frequency
in kHz
Average normalized power
in volts2 or watt-ohms
0.7 –
0.6 –
0.5 –
0.4 –
0.3 –
0.2 –
0.1 –
0.5 1
1.5 2
Frequency
in kHz

5. Relevance of Average Normalized Power (Example 2.10)
The percentage of average normalized power that
lies within the bandwidth of the channel (called the
in-band power) is related to the distortion caused by
the channel.

6. Channel with 300 Hz bandwidth passes 88% of the signal’s power
Average normalized power
in volts2 or watt-ohms
Frequency
in kHz
0.7 –
0.6 –
0.5 –
0.4 –
0.3 –
0.2 –
0.1 –
0.5 1
1.5 2

7. Channel with 500 Hz bandwidth passes 90% of the signal’s power
0.7 –
0.6 –
0.5 –
0.4 –
0.3 –
0.2 –
0.1 –
0.5 1
1.5 2
Frequency
in kHz
Average normalized power
in volts2 or watt-ohms

8. Channel with 1000 Hz bandwidth passes 95% of the signal’s power
0.7 –
0.6 –
0.5 –
0.4 –
0.3 –
0.2 –
0.1 –
0.5 1
1.5 2
Average normalized power
in volts2 or watt-ohms
Frequency
in kHz

9. Channel with 1000 Hz bandwidth passes 97.5% of the signal’s power
0.7 –
0.6 –
0.5 –
0.4 –
0.3 –
0.2 –
0.1 –
0.5 1
1.5 2
Average normalized power
in volts2 or watt-ohms
Frequency
in kHz