Is there any tradeoff between voice quality and bandwidth, how?
Yes there is.
The narrower the bandwidth, the less information which can be carried.
The opposite being true - the wider the bandwidth, the more information can be carried.
Take, as an example, an a.m. broadcast station. Frequency separation between channels is, in the U.S.A., 10kHz, and in the U.K. 9kHz.
The maximum bandwidth transmitted must not exceed 10kHz or 9kHz, depending on the country.
For a 10kHz bandwidth, that of each sideband must not exceed 5kHz, or 4.5kHz in the case of 9kHz channel spacing. In practice the actual bandwidth is a little narrower to prevent one station interfering with another.
This means that the maximum audio frequency which an a.m. broadcast station can transmit is either 4.5kHz or 4kHz depending on the channel separation.
Now consider television transmissions. There is obviously a lot more information to carry and the bandwidth must therefore be much wider.
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