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Nyquist Theorem (Nyquist's Theorem) and Shannon Theorem (Shannon's Theorem) are two basic theorems in network transmission. These two days to review the wireless network, think about it from the basic bar, review things in words to write down, sum up, sort out ideas.

To understand these two theorems, we need to understand some definitions: baud rate (baud rate), bit rate (bit rate), bandwidth (bandwidth), capacity (capacity).

The first two are easily confused definitions (who makes the names of the two brothers look so similar). The baud rate refers to the number of changes in the level of the signal per second, in Hz: for example, if the level of a signal changes 365 times in a second, then the baud rate of the signal is 365Hz. The bit rate is the number of bits of data transmitted by the signal per second. We know that in the computer, the data is represented by zero and one, so the bit rate is the number of zeros and ones transmitted per second, in bps (bit per second). So what's the relationship between the two brothers? We can assume that a signal has only two levels, then the low level can be understood as "0" and the high level as "1", so that the number of changes in the level per second is one number of transmitted zero levels, that is, bit rate = baud rate. But some signals may have more than two levels, such as a four-level signal, so that each level can be understood as "00", "01", "10", "11", so that two-digit data can be transmitted with each level change. that is, bit rate = 2 × baud rate. In general, bit rate = buad rate × log2L, where L is the number of signal levels.

After introducing the two brothers, let's take a look at the concepts of bandwidth and capacity. The general channel has the highest signal frequency (note that it is not the baud rate, the frequency refers to the number of cycles per second, and there are several level changes in each cycle. Well, see the difference between) and the lowest signal frequency, only the signal between these two frequencies can pass through this channel, the difference between these two frequencies is called the bandwidth of this channel, in Hz. What about the capacity of the channel? We know that data transmission in the channel will have their speed-bit rate, in which the highest bit rate is called the capacity of the channel, in bps. It is as if every highway has its maximum speed limit, so all cars driving in it will not exceed that speed (here we assume that the violators have been arrested by the police uncle). In spoken language, the channel capacity will also be called "bandwidth", such as "network with 10m bandwidth", "network bandwidth is 10m" and so on. So the two concepts are easily confused: what we usually call "bandwidth" is not bandwidth, but channel capacity.

Well, after introducing the definition, let's take a look at what these two theorems say.

Nyquist theorem:

Cmax=2 × B × log2L

Here Cmax refers to the maximum capacity of the channel, B is the bandwidth of the channel, L is the number of signal levels.

The Nyquist theorem is applicable to noise-free channels, which are used to calculate theoretical values. There is still a sound when a needle falls on the ground. a channel without noise does not exist in reality. So how to calculate the noisy channel?

Now it's Shannon's turn to come out:

Cmax=B × log2 (1 + (Sramp N))

Snap N refers to the signal-to-noise ratio of the channel, but what we usually measure in terms of db is converted by 10 × log10. So we have to convert it back here.

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