In OFDM the subcarrier pulse used for transmission is chosen to be rectangular. This has the advantage that the task of pulse forming and modulation can be performed by a simple Inverse Discrete Fourier Transform (IDFT) which can be implemented very efficiently as a I Fast Fourier Transform (IFFT). Accordingly in the receiver we only need a FFT to reverse this operation. According to the theorems of the Fourier Transform the rectangular pulse shape will lead to a sin(x)/x type of spectrum of the subcarriers (see figure 0.5).
Figure 0.5: OFDM and the orthogonality principle
Obviously the spectrums of the subcarriers are not separated but overlap. The reason why the information transmitted over the carriers can still be separated is the so called orthogonality relation giving the method its name. By using an IFFT for modulation we implicitly chose the spacing of the subcarriers in such a way that at the frequency where we evaluate the received signal (indicated as arrows) all other signals are zero. In order for this orthogonality to be preserved the following must be true:
is longer than the
maximum channel delay 
all reflections of previous symbols are removed and the orthogonality is preserved.
Of course this is not for free, since by preceding the useful part of length 
by the guard interval we lose some
parts of the signal that cannot be used for transmitting information.
Taking all this into account the signal model for the OFDM transmission over a multipath channel becomes very
simple: The transmitted symbols at time-slot l and subcarrier k are only disturbed by a factor 
which
is the channel transfer function (the fourier transform of the cir) at the subcarrier frequency, an by additional
white Gaussian noise n
The influence of the channel can easily be removed dividing by .
As far as the analog components are concerned experience has shown that in the broadcasting applications under consideration here, they are not so critical. What remains is to establish 'perfect' synchronization. This requires a very sophisticated receiver. The general structure and the receiver of such a receiver which we have developed for the DVB-T application, will be outlined in the next section.
