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The Shannon’s Theorem sets limit on the
- a)Highest frequency that may be sent over channel
- b)Maximum capacity of a channel with a given noise level
- c)Maximum number coding levels in a channel
- d)Maximum number of quantizing levels in a channel
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The Shannon’s Theorem sets limit on thea)Highest frequency that ...
Shannon–Hartley theorem:
It states the channel capacity C, i.e. the theoretical highest upper bound on the information rate of data that can be communicated at an arbitrarily low error rate using an average received signal power S through an analog communication channel that is subject to additive white Gaussian noise (AWGN) of power N.
Mathematically, it is defined as:
C = Channel capacity
B = Bandwidth of the channel
S = Signal power
N = Noise power
∴ It is a measure of capacity on a channel. And it is impossible to transmit information at a faster rate without error.
So that Shannon’s Theorem sets limit on the maximum capacity of a channel with a given noise level.
The Shannon–Hartley theorem establishes that the channel capacity for a finite-bandwidth continuous-time channel is subject to Gaussian noise.
It connects Hartley's result with Shannon's channel capacity theorem in a form that is equivalent to specifying the M in Hartley's line rate formula in terms of a signal-to-noise ratio, but achieving reliability through error-correction coding rather than through reliably distinguishable pulse levels.
Bandwidth and noise affect the rate at which information can be transmitted over an analog channel.
Bandwidth limitations alone do not impose a cap on the maximum information rate because it is still possible for the signal to take on an indefinitely large number of different voltage levels on each symbol pulse, with each slightly different level being assigned a different meaning or bit sequence.
Taking into account both noise and bandwidth limitations, however, there is a limit to the amount of information that can be transferred by a signal of a bounded power, even when sophisticated multi-level encoding techniques are used.
In the channel considered by the Shannon–Hartley theorem, noise and signal are combined by addition. That is, the receiver measures a signal that is equal to the sum of the signal encoding the desired information and a continuous random variable that represents the noise.
It states the channel capacity C, i.e. the theoretical highest upper bound on the information rate of data that can be communicated at an arbitrarily low error rate using an average received signal power S through an analog communication channel that is subject to additive white Gaussian noise (AWGN) of power N.
Mathematically, it is defined as:
C = Channel capacity
B = Bandwidth of the channel
S = Signal power
N = Noise power
∴ It is a measure of capacity on a channel. And it is impossible to transmit information at a faster rate without error.
So that Shannon’s Theorem sets limit on the maximum capacity of a channel with a given noise level.
The Shannon–Hartley theorem establishes that the channel capacity for a finite-bandwidth continuous-time channel is subject to Gaussian noise.
It connects Hartley's result with Shannon's channel capacity theorem in a form that is equivalent to specifying the M in Hartley's line rate formula in terms of a signal-to-noise ratio, but achieving reliability through error-correction coding rather than through reliably distinguishable pulse levels.
Bandwidth and noise affect the rate at which information can be transmitted over an analog channel.
Bandwidth limitations alone do not impose a cap on the maximum information rate because it is still possible for the signal to take on an indefinitely large number of different voltage levels on each symbol pulse, with each slightly different level being assigned a different meaning or bit sequence.
Taking into account both noise and bandwidth limitations, however, there is a limit to the amount of information that can be transferred by a signal of a bounded power, even when sophisticated multi-level encoding techniques are used.
In the channel considered by the Shannon–Hartley theorem, noise and signal are combined by addition. That is, the receiver measures a signal that is equal to the sum of the signal encoding the desired information and a continuous random variable that represents the noise.
Most Upvoted Answer
The Shannon’s Theorem sets limit on thea)Highest frequency that ...
Maximum capacity of a channel with a given noise level
The Shannon's Theorem, formulated by Claude Shannon in 1948, establishes a fundamental limit on the maximum rate at which information can be reliably transmitted over a communication channel. This limit is known as the channel capacity.
Explanation:
- The maximum capacity of a channel is determined by the bandwidth of the channel and the level of noise present in the channel.
- Shannon's Theorem mathematically defines the maximum achievable data rate, or capacity, of a channel in the presence of noise. It states that for a given channel bandwidth and noise level, there exists a maximum rate at which data can be transmitted reliably.
- The channel capacity is the maximum rate at which information can be transmitted over a channel while maintaining a specified error rate. It takes into account the channel's bandwidth, signal-to-noise ratio, and other relevant parameters.
- By determining the maximum capacity of a channel, Shannon's Theorem provides a theoretical upper limit on the data rate that can be achieved in practical communication systems.
- Engineers use the channel capacity calculated based on Shannon's Theorem as a benchmark for designing communication systems to ensure efficient and reliable data transmission.
In conclusion, Shannon's Theorem sets a limit on the maximum capacity of a channel with a given noise level, providing valuable insights for the design and optimization of communication systems.
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