Final answer:
The ratio of bits per Hertz when transmitting 100 digitized voice channels at 64Kbps each over a 20 KHz pass-band without a guard band is 320 bits/Hz.
Step-by-step explanation:
The question is about transmitting 100 digitized voice channels using frequency-division multiplexing (FDM) through a 20 KHz pass-band channel. Each voice channel has a data rate of 64Kbps. To calculate the ratio of bits/Hz without a guard band, we first need to determine the total required bandwidth for all channels, then divide this by the channel bandwidth.
Total bandwidth needed for 100 channels is 100 channels * 64 Kbps/channel = 6400 Kbps. Since we have only a 20 KHz pass-band channel and we wish to know the bits/Hz efficiency, we can simplify units by converting Kbps to KHz for a direct comparison since 1 bps = 1 Hz in digital channels under certain conditions (a direct result of Nyquist theorem which is beyond the scope of this problem). Thus, we have a total bandwidth of 6400 Kbps which is equivalent to 6400 KHz.
Now, divide the total bandwidth in KHz by the pass-band bandwidth in KHz to find the ratio of bits/Hz:
Ratio of bits/Hz = 6400 KHz / 20 KHz = 320 bits/Hz.
Therefore, without using a guard band, we would have a ratio of 320 bits per Hertz for the transmission.