# Exercise 1.1Z: ISDN Connection

We consider the scenario shown in the picture:

A woman from Munich dials a number in Hamburg with her ISDN phone.  However, she cannot reach the person she wants to talk to, so she leaves him a message on tape.

The distortion-free connection is fully described by

• an attenuation coefficient   $\alpha$,
• a term  $\tau$  and
• the current signal-to-noise ratio (SNR).

Notes:  The task shall establish a relation between this real scenario and the functional units of a general communications system mentioned in the theory section .

### Questions

1

Which of the statements are true regarding source and transmitter?

 The message source is the caller.  The source signal  ${q(t)}$  is the acoustic wave of her voice signal. The unit labelled  "transmitter"  contains, among other things, a signal converter and a modulator. The transmitted signal  $s(t)$  is analog.

2

Which of the statements are true regarding receiver and sink?

 The received signal  $r(t)$  is digital. The message sink is the telephone set in Hamburg. The message sink is the answering machine. The following applies:  $v(t) = \alpha \cdot q(t - \tau ) + {n(t)}$. There is an ideal transmission system.

### Solution

#### Solution

(1)  The first two statements are correct:

• The speech signal  ${q(t)}$  must first be converted into an electrical signal and then prepared for transmission.
• For ISDN the transmitted signal  ${s(t)}$  is digital.

(2)  Correct are the solutions 3 and 4:

• The received signal  ${r(t)}$  is always analog due to the unavoidable thermal noise.
• The message sink is the answering machine.
• In an ideal transmission system  $v(t) = {q(t)}$  should apply.
• However,  due to the additive noise term  ${n(t)}$,  the attenuation  $\alpha$  and the delay time  $\tau$  the following applies here:
$$v(t) = \alpha \cdot q ( t - \tau) + n(t).$$
• By our definitions, this is a distortion-free system.