0.1 A telecommunication system  (Page 7/15)

This procedure is shown diagrammatically in [link] . The spectrum of the original message is shown in (a), andthe spectrum of the message modulated by the carrier appears in (b). When downconversion is done as just described, the demodulated signal $d\left(t\right)$ has the spectrum shown in (c). Filtering by a lowpass filter (as in part (c)) removes all but a scaled version of the message.

Now consider the FDM transmitted signal spectrum of [link] . This can be demodulated/downconverted similarly.The frequency-shifting rule [link] , with a shift of $f_0=f_3$ , ensures that the downconverted spectrum in [link] matches [link] , and the lowpass filter removes all but the desired message from the downconverted signal.

This is the basic principle of a transmitter and receiver pair. But there are some practical issues that arise.What happens if the oscillator at the receiver is not completely accurate in eitherfrequency or phase? The downconverted received signal becomes $s\left(t\right)\cos (2\pi (f_0+\alpha )t+\beta )$ . This can have serious consequences for the demodulated message.What happens if one of the antennas is moving? The Doppler effect suggests that this corresponds toa small nonzero value of $\alpha$ . What happens if the transmitter antenna wobblesdue to the wind over a range equivalent to several wavelengths of the transmitted signal?This can alter $\beta$ . In effect, the baseband component is perturbed from $(1/2)W\left(f\right)$ , and simply lowpass filtering the downconverted signal results in distortion.Carrier synchronization schemes (which attempt to identifyand track the phase and frequency of the carrier) are routinely used in practice to counteract such problems.These are discussed in detail in [link] and [link] .

Analog core of a digital communication system

The signal flow in the AM communication system described in the preceding sectionsis shown in [link] . The message is upconverted (for efficient transmission), summed withother FDM users (for efficient use of the electromagnetic spectrum), subjected to possible channel noises (such as thermal noise),bandpass filtered (to extract the desired user), downconverted (requiring carrier synchronization), and lowpass filtered(to recover the actual message).

But no transmission system operates perfectly. Each of the blocks in [link] may be noisy, may have components which are inaccurate, and may be subject to fundamentallimitations. For instance,

• the bandwidth of a filter may be different from its specification (e.g., the shoulders may not dropoff fast enough to avoid passing some of the adjacent signal),
• the frequency of an oscillator may not be exact, and hence the modulation and/or demodulation may not be exact,
• the phase of the carrier is unknown at the receiver, since it depends on the time of travel between the transmitterand the receiver,
• perfect filters are impossible, even in principle,
• no oscillator is perfectly regular, there is always some jitter in frequency.