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Unformatted text preview: e t o t hose of Hertz a nd Marconi. I t was largely t he work of Armstrong
t hat was responsible for rekindling t he i nterest in FM. Lamentably, Armstrong, who
became despond€nt over the lengthy, most acrimonious, and expensive court battles
with some t itans of t he c ommunication industry over his p atent rights, committed
suicide in 1954 b y walking o ut of a window 13 stories above t he s treet. 4.9 D ata T runcation: Window Functions 301 We 4 .8-4 (a) (b) Transmitter Bandpass
filter Frequency-Division Multiplexing Signal m ultiplexing allows transmission of several signals on t he s ame channel.
In C hapter 5, we shall discuss time-division multiplexing (TDM), where several
signals time-share t he same channel, such as a cable or a n optical fiber. In frequencydivision multiplexing (FDM), t he use of modulation, as illustrated in Fig. 4.45,
makes several signals share t he b and of t he s ame channel. Each signal is m odulated
by a different c arrier frequency. T he various carriers are adequately separated to
avoid overlap ( or interference) between t he s pectra of various modulated signals.
These carriers a re referred to as s ub c arriers. Each signal may use a different kind
of modulation (for example, DSB-SC, AM, SSB-SC, VSB-SC, or even F M or PM).
T he m odulated-signal s pectra m ay be separated by a small guard b and t o avoid
interference a nd facilitate signal separation a t t he receiver.
W hen all o f t he m odulated s pectra a re added, we have a composite signal t hat
m ay be considered as a baseband signal. Sometimes, this composite baseband signal
may be used t o f urther modulate a high-frequency (radio frequency, or RF) carrier
for t he p urpose o f transmission.
At t he receiver, t he incoming signal is first demodulated by t he R F c arrier t o
r etrieve t he c omposite baseband, which is t hen b andpass filtered t o s eparate each
modulated signal. T hen each modulated signal is individually demodulated by an
appropriate sub carrier to obtain all t he basic baseband signals. 4 .9 01 Data Truncation: Window Functions
We often need t o t runcate d ata in diverse situations from numerical computa- F ig. 4 .45 Frequency division multiplexing. tions t o filter design. For example, if we need t o c ompute numerically t he Fourier
transform of some Signal, say e -tu(t), on a computer, we will have to t runcate t he
signal e -tu(t) beyond a sufficiently large value of t (typically five t ime constants
and above). T he reason is t hat in numerical computations, we have t o deal with
d ata of finite duration. Similarly, t he impulse response h (t) of an ideal lowpass
filter is noncausal, a nd approaches zero asymptotically as It I - > 0 0. For a practical
design, we m ay want t o t runcate h(t) b eyond a sufficiently large value of It I t o make
h(t) causal. In signal sampling, t o e liminate aliasing, we need to t runcate t he signal
s pectrum b eyond t he h alf sampling frequency w s /2, using an anti-aliasing filter. 302 4 Continuous-Time Signal Analysis: T he Fourier Transform 4.9 D ata Truncation: Window Functions Again, we may w ant t o synthesize a peri...
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