**Any signal can be transmitted in an electrical form as an analogue or digital signal. As we know from another courses, analogue signal is a continuous time signal and can take a countless number of values; digital is a discrete-time signal and can take only several values.**

In a binary system there are two values – 1 or 0, ON and OFF, or TRUE or FALSE. Each bit lasts for the *bit slot* period of time *T _{B}*. The

*bit rate*$B=\frac{1}{{T}_{B}}$ is the number of bits per second. Analogue and digital signals are characterised by bandwidth. Signal bandwidth is the range of frequencies contained in the signal, which can be determined from the signal’s Fourier transform.

Analogue signal can be converted into a digital form, with the sampling method (this method was mentioned in the course of the Signals and Systems module). The sampling rate is determined by the analogue signal bandwidth *Δf*. The bandwidth limited analogue signal can be represented with discrete intervals without information losses. The sampling frequency satisfies the Nyquist criterion ƒ_{s} > *2Δf*.

During sampling *quantisation noise* may occur. This noise usually adds to the analogue signal noise. This quantisation noise can be minimised if the quantity of discrete levels will be bigger than the signal dynamic range. $DL>\frac{{A}_{max}}{{A}_{N}}$

where* A _{max}* is the signal amplitude,

*A*is the root-mean-square of the analogue signal. The signal dynamic range is related to the signal-to-noise ratio (SNR), that is measured with decibels (dB): $SNR=20{\mathrm{log}}_{10}\left(\frac{{A}_{max}}{{A}_{N}}\right)$

_{N }There are several conversion schemes that show how to convert the quantised sample values into the digital signal. The *pulse-position modulation* and *pulse-duration modulation* schemes are not used widely. The scheme *pulse-code modulation (PCM)* is widely used for conversion. PCM method is based on the binary scheme. The number of bits *m = log _{2} M* is needed to code each sample, where

*M*is the number of quantised signal levels. The bit rate associated with the PCM digital signal is:

The bit rate *B* is the minimum needed to digitalise the analogue signal with the bandwidth *Δf *and specific SNR. The digital format is used for optical communications.

Most fibre optic communicating systems transmit at a rate of *1Gb/s*. It is necessary to transmit many channels simultaneously by multiplexing. This can be done with two techniques: *TDM* or *time-division multiplexing *and *FDM* or *frequency division multiplexing*.

In TDM technique bits are associated to different channels, and are interleaving in a time domain to form a proper bit stream. TDM is fine for digital signals and is used for telecommunication networks. In FDM technique channels are spaced apart in the frequency domain. Each channel is carried by it’s own carrier wave. The carrier frequencies are located wider than the channel bandwidth. FDM is fine for both analogue and digital signals and is used for the broadcasting of radio and television. TDM and FDM can be used in electrical and optical domains. The optical domain of FDM is called as WDM.

The idea of TDM is the basis for digital hierachies, and the technology of data transmission. The technologies used now are *SONET* or *synchronous optical network *and *SHD *or *synchronous digital hierarchy.* These technologies determines the frame structure of TDM digital signals. Table 1 (below) shows SONET/SDH bit rates.

SONET signal | SDH signal | Optical carrier | Bit rate, Mbps | Channels |

STS-1 | 51.84 | 672 | ||

STS-3 | STM-1 | OC-3 | 155.52 | 2,016 |

STS-12 | STM-4 | OC-12 | 622.08 | 8,064 |

STS-48 | STM-16 | OC-48 | 2,488.32 | 32,256 |

STS-192 | STM-24 | OC-192 | 9,953.28 | 129,024 |

STS-768 | STM-256 | OC-768 | 39,814.32 | 516m096 |