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

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)

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

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

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.

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

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

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

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