# The relationship between information bandwidth and noise

The Relationship Between Data Rate Capacity, Noise, and Frequency Bandwidth (Morikawa). The maximum data rate capacity of a digital communications. I would like to pay your attention that there are some information missed to There is inverse relation between SNR (Signal to Noise Ratio) and BER (Bit BER=, SINR(Signal to Noise + Interference)=, B(Bandwidth)=3 MHz, R= A given communication system has a maximum rate of information C known as where C is the capacity in bits per second, B is the bandwidth of the channel in Hertz, and S/N is the signal-to-noise ratio. . This relationship is as follows: −5. 0.

## Shannon–Hartley theorem

The converse is also important. So no useful information can be transmitted beyond the channel capacity. The theorem does not address the rare situation in which rate and capacity are equal. The Shannon—Hartley theorem establishes what that channel capacity is for a finite-bandwidth continuous-time channel 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. If there were such a thing as a noise-free analog channel, one could transmit unlimited amounts of error-free data over it per unit of time Note: An infinite-bandwidth analog channel can't transmit unlimited amounts of error-free data, without infinite signal power.

Real channels, however, are subject to limitations imposed by both finite bandwidth and nonzero noise. Bandwidth and noise affect the rate at which information can be transmitted over an analog channel.

### Noise, Data Rate and Frequency Bandwidth

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.

It is considered "idealized" since environmental influences, particularly noise, is not considered. In order to enter this problem into your calculator, you should use the following conversion: Shannon-Hartley developed a similar equation for capacity; however they included the Signal-to-Noise ratio SNR which provides a slightly more realistic answer. Shannon-Hartley's equation provides the "theoretical" maximum capacity for a signal given its frequency bandwidth and SNR.

Typically, digital communication systems do not reach this theoretical capacity due to many factors such as modulation scheme and the overall noise environment. SNR is the ratio of the received power in watts, to thermal noise. Noise other than thermal, such as impulse, interference from other sources, etc. So it's worth taking a closer look at what thermal noise is.

### Shannon–Hartley theorem - Wikipedia

Thermal noise is caused by the agitation of electrons in a material. As temperature increases, so does the agitation or activity of the electrons, thus resulting in greater thermal noise. This noise impacts our ability to distinguish signal power from noise power. Since electrons exist in all materials, the noise produced cannot be eliminated. Thermal noise spans across all frequencies and is usually called the "noise floor".