Consider a noiseless channel with a bandwidth of 5000Hz transmitting a signal with two signal levels. The maximum bit rate is

The correct answer is 10000 bps.

Key Points

• According to the Nyquist formula for a noiseless channel, the maximum bit rate can be calculated as:
  • Bit Rate = 2 * Bandwidth * log₂(L)
  • Where L is the number of signal levels.
  • In this case, the bandwidth is 5000 Hz and there are 2 signal levels.
  • Substituting the values, we get:
    • Bit Rate = 2 * 5000 * log₂(2)
    • log₂(2) is 1.
    • Therefore, Bit Rate = 2 * 5000 * 1 = 10000 bps
• Hence, the maximum bit rate is 10000 bps.

Additional Information

• The Nyquist theorem is fundamental in digital communications for determining the maximum data rate of a noiseless channel.
• This theorem is particularly useful in understanding the limitations of signal transmission in various communication systems.
• Practical implementations may achieve lower bit rates due to various factors such as noise and signal attenuation.
• The number of signal levels (L) directly influences the bit rate; higher levels can increase the bit rate, but also increase complexity and potential error rates.