# The Physical Layer

The physical layer defines the electrical, temporal, and other interfaces through which bits are sent as signals via channels. The physical layer is the base on which the network is built. The properties of different types of physical channels determine performance (for example, performance, delay, and error rates). There are three examples of communication systems used in practice for large computer networks (WAN):

- A (fixed) telephone system,
- A mobile telephone system
- A cable television system

The information can be transmitted via cables that modify certain physical properties, such as current or voltage. By presenting the value of this voltage or current as a function of the unique time value f (t), we can simulate the behavior of our signal and analyze it mathematically.

**Fourier Analysis**

Any periodic function of the reasonable behavior g (t) with the period T can be constructed as the sum of the number (infinite possible) of sines and cosines.

where f = 1 / T is the fundamental frequencies and are the cosines and sines of the amplitude of the n-th harmonic. This decomposition is called the Fourier series. A data signal having a finite duration can be processed simply by imagining that it repeats the entire pattern again and again forever.

**Bandwidth Limited Signal**

The urgency of all this for data transmission is that the actual channels affect the different frequency signals in different ways. No transmission medium can transmit signals without loss of power in the process. If all Fourier components were reduced equally, the resulting signal amplitude would decrease, but would not be distorted.

Unfortunately, all the transmission means reduce the various Fourier components to varying degrees, resulting in distortion. As a general rule, for the cable or wire, the amplitudes are mainly transmitted without decay from 0 to any frequency FC [measured in cycles per second or Hertz (Hz)], all frequencies above this attenuated cutoff frequency.

The width of the transmitted frequency range without strong attenuation is called the bandwidth. Bandwidth is a physical property of the transmission medium, which depends, for example, on the design, thickness, and length of the cable or fiber. Filters are often used to further limit the bandwidth of a signal. 802.11 wireless channels can use, for example, up to 20 MHz Thus, 802.11 radios filter the signal bandwidth at that size.

Bps |
T (msec) |
First harmonic (Hz) |
# Harmonics sent |

300 | 26.67 | 37.5 | 80 |

600 | 13.33 | 75 | 40 |

1200 | 6.67 | 150 | 20 |

2400 | 3.33 | 300 | 10 |

4800 | 1.67 | 600 | 5 |

9600 | 0.83 | 1200 | 2 |

19200 | 0.42 | 2400 | 1 |

38400 | 0.21 | 4800 | 0 |

**The Maximum Data Rate of a Channel**

Henry Nyquist realized that even the ideal channel has limited bandwidth. An equation expressing the maximum data transfer rate for a silent channel with a finite bandwidth is obtained.

Nyquist showed that if an arbitrary waveform was transmitted via the low-pass filter of bandwidth B, the filtered signal could be fully restored with only 2 (accurate) samples received per second. Sampling a line faster than 2B once a second does not make sense because components with a higher frequency than such a sample can restore are already deleted. If the signal consists of V discrete levels, the Nyquist theorem says:

maximum data rate = 2*B *log2 *V *bits /sec

“The continuous-time signal can be fully represented in your samples and restored if the sampling rate is greater than or equal to twice the maximum frequency”. The amount of thermal noise present is measured by the ratio between the signal power (in dB) and the noise power, called the signal-to-noise ratio.

The main result of Shannon is that the data transfer rate or the maximum noise channel capacity, whose bandwidth is B Hz, and the signal-to-noise ratio S / N, are defined as follows:

maximum number of bits/sec = *B *log2 (1 + *S/N*)