2.1 Information and Information Transmission

|

7

Tab. 2.1: Data rates of common signals.

Type

data rate

Eye

100 Mbit/s

Ear

50 kbit/s

Language

64 kbit/s

Audio CD (44.1 kHz, 16 bit)

700 kbit/s

Bluetooth

25 Mbit/s

However, these theoretical data rates are never achieved in practice, the reasons for

this are on the one hand the available bandwidth of the transmission channel and on

the other hand the existing interference on the transmission path (cf. Figure 2.1). A

Inf. Source

Transmitter

Transmission channel

Receiver

Inf. Destination

Interference

Fig. 2.1: Transmission path of information transmission under the influence of interference.

maximum data transmission rate Cmax can be calculated using the Shannon-Hartley

law as a function of the bandwidth B and the signal to noise ratio or signal-noise ratio

SNR as follows:

Cmax = B ⋅log2(1 + SNR) .

(2.3)

Signal-to-Noise Ratio

In electrical engineering, the signal-noise-ratio is the ratio of the average power of the

desired signal Psignal to the average noise power of the interfering signal Pnoise. The

average electric power of an AC circuit with resistive load R, instantaneous voltage u

and instantaneous current i, is defined as P = u ⋅i. Using Ohm’s law i = u/R, the

following relationship can be established for averaging over the period T = t0, . . . , t1:

P = u ⋅i = ¹

T

t1

∫

t0

u ⋅i dt = ¹

T

t1

∫

t0

1

R ^{u2 dt .}

(2.4)

The effective value of an alternating quantity is the value of a current or a voltage

at which a resistive load converts the same electrical power in a representative time

T = t1 −t0 as a corresponding direct quantity. This means that the converted average

power of the instantaneous values in the period t0, . . . , t1 corresponds exactly to the