Coded Orthogonal Frequency Division Multiplex (COFDM) - Digital Video and Audio Broadcasting Technology - page 318

Varying the period ∆t of the rectangular pulse varies the spacing ∆f of
the nulls in the spectrum. If ∆t is allowed to tend towards zero, the nulls in
the spectrum will tend towards infinity. This results in a Dirac pulse which
has an infinitely flat spectrum which contains all frequencies. If ∆t tends
towards infinity, the nulls in the spectrum will tend towards zero. This re-
sults in a spectral line at zero frequency which is DC. All cases in between
simply correspond to

∆f = 1/∆t;

A train of rectangular pulses of period T p and pulse width ∆t also corre-
sponds to this sin(x)/x-shaped variation but there are now only discrete
spectral lines spaced apart by f P = 1/T P which, however, conform to this
sin(x)/x-shaped variation.
What then is the relationship between the rectangular pulse and or-
thogonality? The carrier signals are sinusoidal. A sinewave signal of fre-
quency f S = 1/T S results in a single spectral line at frequency f S and -f S in
the frequency domain. However, these sinusoidal carriers carry informa-
tion by amplitude- and frequency-shift keying.

f

Carrier spacing

f

Channel bandwidth

Fig. 19.6. Coded Orthogonal Frequency Division Multiplex (COFDM)

I.e., these sinusoidal carrier signals do not extend continuously from
minus infinity to plus infinity but change their amplitude and phase after a
particular time ∆t. Thus one can imagine a modulated carrier signal to be
composed of sinusoidal sections cut out rectangularly, so-called burst