fft in Constant 2009
8
Late in the encoding process, and much earlier in the decoding
process in contemporary wireless networks, a fairly generic computational algorithm comes into action: the Fast Fourier Transform
(ffT). In some ways, it is not surprising to find the ffT in wireless networks or in digital video. Dating from the mid-1960s, ffTs
have long been used to analyse electrical signals in many scientific
and engineering settings. It provides the component frequencies of
a time-varying signal or waveform. Hence, in ‘spectral analysis', the
ffT can show the spectrum of frequencies present in a signal.
The notion of the Fourier transform is mathematical and has been
known since the early 19th century: it is an operation that takes
an arbitrary waveform and turns it into a set of periodic wav
pproaches I
described earlier. Once a complex signal, such as an image, has been
analysed into a set of static components, we can imagine code that
4
Humanities and social science work on the Fast Fourier Transform is hard to find, even
though the ffT is the common mathematical basis of contemporary digital image,
video and sound compression, and hence of many digital multimedia (in JPEG, MPEG
files, in DVDs). In the early 1990s, Friedrich Kittler wrote an article that discussed
it {Kittler, 1993 #753}. His key point was largely to show that there is no realtime
in digital signal processing. The ffT works by defining a sliding window of time for
a signal. It treats a complicated signal as a set of blocks that it lifts out of the time
domain and transforms into the frequency domain. The ffT effectively plots an event
in time as a graph in space. The experience of realtime is epiphenomenal. In terms of
the ffT, a signal is always partly in the future or the past. Although Kittler was not
referring to the use of ffT in wireless networks, the same point applies – there is no
realtime communication. However, while this point about the impossibility of realtime
calculation was important to make during the 1990s, it seems well-established now.
168
168
168
169
169
would select the most important or relevant components. This is precisely what happens in video and sound codecs such as MPEG and
MP3.
The ffT treats sounds and images as complicated superimpositions of waveforms. The envelope of a signal becomes something that
contains many simple signals. It is interesting that wireless networks
tend to use this process in reverse. It deliberately takes a well-separated and discrete set of signals – a digital datastream – and turns it
into a single complex signal. In contrast to the normal uses of ffT in
separating important from insignificant parts of a signal, in wireless
networks, and in many other communications setting, ffT is used to
put signals together in such a way as to contain them in a single envelope. The ffT is found in many wireless computation algorithms
because it allows many different digital signals to be put together on
a single wave and then extracted from it again.
Why would this superimposition of many signals onto a single complex waveform be desirable? Would it not increase the possibilities of
confusion or interference between signals? In some ways the ffT is
used to slow everything down rather than speed it up. Rather than
simply spatialising a duration, the ffT as used in wireless networks
defines a different way of inhabiting the crowded, noise space of electromagnetic radiation. Wireless transmitters are better at inhabiting
crowded signal spectrum when they don't try to separate themselves
off from each other, but actually take the presence of other transmitters into account. How does the ffT allow many transmitters to
inhabit the same spectrum, and even use the same frequencies?
The name of this technique is OFDM (Orthogonal Frequency Division Multiplexing). OFDM spreads a single data stream coming
from a single device across a large num
paced apart more in time. This has great advances in urban
environments where there are many obstacles to signals, and signals
can reflect and echo often. In this context, the slower the data is
transmitted, the better.
At the transmitter, a reverse ffT (IffT) is used to re-combine
the 50 signals onto 1 signal. That is, it takes the 50 or so different
sub-carriers produced by OFDM, each of which has a single slightly
different, but carefully chosen frequency, and combines them into one
complex signal that has a wide spectrum. That is, it fills the available
spectrum quite evenly because it contains many different frequency
components. The waveform that results from the IffT looks like
'white noise': it has no remarkable or outstanding tendency whatsoever, except to a receiver synchronised to exactly the right carrier
frequency. At the receiver, this complex signal is transformed, using ffT, back into a set of 50 separate data streams, that are then
reconstituted into a single high speed stream.
Even if we cannot come to grips with the techniques of transformation using in DSP in any great detail, I hope that one point stands
out. The t
Display 200 300 400 500 600 700 800 900 1000 ALL characters around the word.