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\PlaceImage{mackenzie02.JPG}{Adrian Mackenzie at V/J10}

\AuthorStyle{Adrian Mackenzie}

\licenseStyle{Creative Commons Attribution{}-NonCommercial{}-ShareAlike}

\Flag{EN}\Title{Centres of envelopment and intensive movement in digital signal processing}

\SubSubTitle{Abstract}

{\em The paper broadly concerns algorithmic processes commonly found in
wireless networks, video and audio compression. The problem it
addresses is how to account for the convoluted nature of the digital
signal processing (DSP). Why is signal processing so complex and
relatively inaccessible? The paper argues that we can only understand
what is at stake in these labyrinthine calculations by switching focus
away from abstract understandings of calculation to the dynamic
re{}-configuration of space and movement occurring in signal
processing. The paper works through one example in detail of this
reconfigured movement in order to illustrate how digital signal
processing enables different experiences of proximity, intimacy,
co{}-location and distance. It explores how wireless signal processing
algorithms envelope heterogeneous spaces in the form of hidden states,
and logistical networks. Importantly, it suggests that the ongoing
dynamism of signal processing could be understood in terms of intensive
movement produced by a centre of envelopment. Centres of envelopment
generate extensive changes, but they also change the nature of change
itself.}

\SubSubTitle{From sets to signals: digital signal processing}

In new media art, in new media theory and in various forms of media
activism, there has been so much work that seizes on the possibilities
of using digital technologies to design interactions, sound, image,
text, and movement that challenge dominant forms of experience, habit
and selfhood. In various ways, the processes of branding,
commodification, consumption, control and surveillance associated with
contemporary media have been critically interrogated and challenged. 

However, there are some domains of contemporary technological and media
culture that are really hard to work with. They may be incredibly
important, they may be an intimate part of everyday life, yet remain
relatively intractable. They resist contestation, and engagement with
may even seem pointless. This is because they may contain intractable
materials, or be organised in such complicated ways that they are hard
to change. 

This paper concerns one such domain, digital signal processing (DSP). I am not saying that new media has not engaged with DSP. Of course it
has, especially in video art and sound art, but there is little work
that helps us make sense of how the sensations, textures, and movements
associated with DSP come to be taken for granted, come to appear as
normal, and everyday, or how they could be contested. 

\PlaceImage{mackenzie4.png}{A promotional video from Intel for the UltraMobilePC}

A promotional video from Intel for the UltraMobilePC \footnote{\Url{http://youtube.com/watch?v=GFS2TiK3AI}}
promotes change in relation to mobile media. Intel, because it makes semiconductors, is highly invested in digital signal processing in
various forms. In any case, video itself is a prime example of
contemporary DSP at work. Two aspects of this promotional video for the
UMPC, the UltraMobile PC, relate to digital signal processing. There is
much signal processing here. It connects the
individual's eyes, mouths and ears to screens that
display information services of various kinds. There is also much
signal processing in the wireless network infrastructures that connect
all these gadgets to each other and to various information services
(maps, calendars, news feeds). In just this example, sound, video,
speech recognition, fibre, wireless and satellite, imaging technologies
in medicine all rely on DSP. We could say a good portion of our
experience is DSP{}-based.

This paper is an attempt to develop a theory of digital signal
processing, a theory that could be used to talk about ways of
contesting, critiquing, or making alternatives. The theory under
development here relies a lot on two notions, \quote{intensive movement} and
\quote{centre of envelopment} that Deleuze proposed in {\em Difference and
Repetition.} However, I want to keep the philosophy in the background
as much as possible. I basically want to argue that we need to ask: why
does so much have to be enveloped or interiorised in wireless or
audiovisual DSP? 

\SubSubTitle{How does DSP differ from other algorithmic processes?}

What can we say about DSP? Firstly, influenced by recent software
studies{}-based approaches (Fuller, Chun, Galloway, Manovich), I think
it is worth comparing the kinds of algorithmic processes that take
place in DSP with those found in new media more generally. Although it
is an incredibly broad generalisation, I think it is safe to say that
DSP does not belong to the {\em set{}-based} algorithms and
data{}-structures that form the basis of much interest in new media
interactivity or design.

DSP differs from set{}-based code. If we think of social software such
as Flickr, Google, or Amazon, if we think of basic information
infrastructures such as relational databases or networks, if we think
of communication protocols or search engines, all of these systems rely
on listing, enumerating, and sorting data. The practices of listing,
indexing, addressing, enumerating and sorting, all concern
{\em sets}. Understood in a fairly abstract way, this is what much
software and code does: it makes and changes sets. Even areas that
might seem quite remote from set{}-making, such as the 3D{}-projective
geometry used in computer game graphics are often reduced
algorithmically to complicated set{}-theoretical operations on shapes
(polygons). Even many graphic forms are created and manipulated using
set operations. 

The elementary constructs of most programming languages reflect this
interest in set{}-making. For instance, networks or, in computer
science terms, {\em graphs}, are visually represented like using
lines and boxes. But in terms of code, they are presented as either
edge or \quote{adjacency lists}, like this: \footnote{\Url{http://www.python.org/doc/essays/graphs/}}


\starttyping
graph = {'A': ['B', 'C'],
         'B': ['C', 'D'],
         'C': ['D'],
         'D': ['C'],
         'E': ['F'],
         'F': ['C']}
\stoptyping

A graph or network can be seen as a list of lists. This kind of
representation in code of relations is very neat and nice. It means
that something like the structure of the internet, as a hybrid of
physical and logical relations, can be recorded, stored, sorted and
re{}-ordered in code. Importantly, it is highly open to modification
and change. Social software, or Web2.0, as exemplified in websites like
Facebook or YouTube also can be understood as massive deployments of
set theory in the form of code. Their sociality is very much dependent
on set making and set changing operations, both in the composition of
the user interfaces and in the underlying databases that make
constantly seek to attach new relations to data, to link identities and
attributes. In terms of activism, and artwork, relations that can be
expressed in the form of sets and operations on sets, are highly
manipulable. They can be learned relatively easily, and they are not
too difficult to work with. For instance, scripts that crawl or scrape
websites have been widely used in new media art and activism.

By contrast, DSP code is not based on set{}-making. It relies on a
different ordering of the world that lies closer to streams of signals
that come from systems such as sensors, transducers, cameras, and that
propagate via radio or cable. Indeed, although it is very widely used,
DSP is not usually taught as part of the computer science or software
engineering. The textbooks in these areas often do not mention DSP. The
distinction between DSP and other forms of computation is clearly
defined in a textbook of DSP:

\QuoteStyle{Digital Signal Processing is distinguished from other areas in computer
science by the unique type of data it uses: {\em signals}. In most
cases, these signals originate as sensory data from the real world:
seismic vibrations, visual images, sound waves, etc. DSP is the
mathematics, the algorithms, and the techniques used to manipulate
these signals after they have been converted into a digital form. {\em (Smith, 2004)}}

While it draws on some of the logical and set{}-based operations found
in code in general, DSP code deals with signals that usually involve
some kind of sensory data {--} vibrations, waves, electromagnetic
radiation, etc. These signals often involve forms of rapid movement,
rhythms, patterns or fluctuations. Sometimes these movements are
embodied in physical senses, such as the movements of air involved in
hearing, or the flux of light involved in seeing. Because they are
often irregular movements, they cannot be easily captured in the forms
of movement idealised in classical mechanics {--} translation,
rotation, etc. Think for instance of a typical photograph of a city
street. Although there are some regular geometrical forms, the way in
which light is reflected, the way shadows form, is very difficult to
describe geometrically. It is much easier, as we will see, to think of
an image as a signal that distributes light and colour in space. Once
an image or sound can be seen as a signal, it can undergo digital
signal processing. 

What distinguishes DSP from other algorithmic processes is its reliance
on {\em transforms} rather than functions. This is a key difference.
The \quote{transform} deals with many values at once. This is important
because it means it can deal with things that are temporal or spatial,
such as sounds, images, or signals in short. This brings algorithms
much closer to sensation, and to what bodies feel. While there is
codification going on, since the signal has to be treated digitally as
discrete numerical values, it is less reducible to the sequence of
steps or operations that characterise set{}-theoretical coding. Here
for instance is an important section of the code used in MPEG video
encoding in the free software ffmpeg package:

\PlaceImage{mackenzie01.JPG}{The simplest mpeg encoder}
\starttyping
**
* @file mpegvideo.c
* The simplest mpeg encoder (well, it was the simplest!).
*

...

* for jpeg fast DCT */

#define CONST_BITS 14
static const uint16_t aanscales[64] = {
    /* precomputed values scaled up by 14 bits */
    16384, 22725, 21407, 19266, 16384, 12873, 8867, 4520,
    22725, 31521, 29692, 26722, 22725, 17855, 12299, 6270,
    21407, 29692, 27969, 25172, 21407, 16819, 11585, 5906,
    19266, 26722, 25172, 22654, 19266, 15137, 10426, 5315,
    16384, 22725, 21407, 19266, 16384, 12873, 8867, 4520,
    12873, 17855, 16819, 15137, 12873, 10114, 6967, 3552,
    8867, 12299, 11585, 10426, 8867, 6967, 4799, 2446,
    4520, 6270, 5906, 5315, 4520, 3552, 2446, 1247
};

...

for(i=0;i<64;i++) {
           const int j=
dsp{}->}idct_permutation[i];
           qmat[qscale][i] = (int)((uint64_t_C(1)
<< (QMAT_SHIFT + 14))
                      (aanscales[i]
* qscale * quant_matrix[j]));
\stoptyping


I don't think we need to understand this code in detail. There is only
one thing I want to point out in this code: the list of \quote{precomputed}
numerical values is used for \quote{jpeg fast DCT}. This is a typical piece
of DSP type code. It refers to the way in which video frames are
encoding using Fast Fourier Transforms. The key point here is that
these values have been carefully worked out in advance to scale
different colour and luminosity components of the image differently.
The transform, DCT (Discrete Cosine Transform), is applied to chunks of
sensation {--} video frames {--} to make them into something that can
be manipulated, stored, changed in size or shape, and circulated.
Notice that the code here is quite opaque in comparison to the graph
data structures discussed previously. This opacity reflects the sheer
number of operations that have to be compressed into code in order for
digital signal processing to work.

\SubSubTitle{Working with DSP: architecture and geography}

So we can perhaps see from the two code examples above that there is
something different about DSP in comparison to the set{}-based
processing. DSP seems highly numerical and quantified, while the
set{}-based code is symbolic and logical. What is at stake in this
difference? I would argue that it is something coming into the code
from outside, something that is difficult to read in the code itself
because it is so opaque and convoluted. Why is DSP code hard to
understand and also hard to write? 

You will remember that I said at the outset that there are some facets
of technological cultures that resist appropriation or intervention. I
think the mathematics of DSP is one of those facets. If I just started
explaining some of the mathematical models that have been built into
the contemporary world, I think it would be shoring up or reinforcing a
certain resistance to change associated with DSP, at least in its main
mathematical formalisations. I do think the mathematical models are
worth engaging with, partly because they look so different from the
set{}-based operations found in much code today. The mathematical
models can tell us why DSP is difficult to intervene in at a low level.

However, I don't think it is the mathematics as such that makes digital
signal processing hard to grapple with. The mathematics is an
{\em architectural} response to a {\em geographical} problem, a
problem of where code can go and be in the world. I would argue that it
is the relation between the {\em architecture} and {\em geography
}of digital signal processing itself that we should grapple with. It is
something to do about the immersion in everyday life, the proximity to
sensation, the shifting multi{}-sensory patterning of sociality, the
movements of bodies across variable distances, and the effervescent
sense of impending change that animates the convoluted architecture of
DSP.

We could think of the situations in which DSP is commonly found. For
instance, in the background of the scenes in the daily lives of
businessmen shown in Intel's UPMC video, lie wireless infrastructures
and networks. Audiovisual media and wireless networks both use signal
processing, but for different reasons. Although they seem quite
disparate from each other in terms of how we embody them, they actually
sometimes use the same DSP algorithms. (In other work, I have discussed
video codecs.\footnote{{\bf The case of video codecs}

In the foreground of the UMPC vision, stand
images, video images in particular, and to a lesser extent, sounds.
They form a congested mass, created by media and information networks.
People in electronic media cultures constantly encounter images in
circulation. Millions of images flash across TV, cinema and computer
screens. DVD's shower down on us. The internet is loaded down with
video at the moment (Google Video, YouTube.com, Yahoo video, etc.). A
powerful media{}-technological imagining of video moving everywhere,
every which way, has taken root. \par The growth of video material
culture is associated with a key dynamic: the proliferation of software
and hardware {\em codecs.} Codecs generate linear
transforms of images and sound. Transformed images move through
communication networks much more quickly than uncompressed audiovisual
materials. Without codecs, an hour of raw digital video would need 165
CD{}-ROMs or take roughly 24 hours to move across a standard computer
network (10Mbit/sec ethernet). Instead of 165 CDs, we take a single DVD
on which a film has been encoded by a codec. We play it on a DVD player
that also has a codec, usually implemented in hardware. Instead of
32Mbyte/sec, between 1{}-10 MByte/sec streams from the DVD into the
player and then onto the television screen. \par
The economic and technical value of codecs can hardly
be overstated. DVD, the transmission formats for satellite and cable
digital television (DVB and ATSC), HDTV as well as many internet
streaming formats such as RealMedia and Windows Media, third generation
mobile phones and voice{}-over{}-ip (VoIP), all depend on video and
audio codecs. They form a primary technical component of contemporary
audiovisual culture. \par Physically, codecs take many forms, in
software and hardware. Today, codecs nestle in set{}-top boxes, mobile
phones, video cameras and webcams, personal computers, media players
and other gizmos. Codecs perform encoding and decoding on a digital
data stream or signal, mainly in the interest of finding what is
different in a signal and what is mere repetition. They scale, reorder,
decompose and reconstitute perceptible images and sounds. They only
move the differences that matter through information networks and
electronic media. This performance of difference and repetition of
video comes at a cost. Enormous complication must be compressed in the
codec itself.\par Much is at stake in this logistics from the
perspective of cultural studies of technology and media. On the one
hand, codecs analyse, compress and transmit images that fascinate,
bore, fixate, horrify and entertain billions of spectators. Many of
these videos are repetitive or clich\'ed. There are many re{}-runs of
old television series or Hollywood classics. YouTube.com, a video
upload site, offers 13,500 wedding videos. Yet the spatio{}-temporal
dynamics of these images matters deeply. They open new patterns of
circulation. To understand that circulation matters deeply, we could
think of something we don't want to see, for instance, the execution of
many hostages (Daniel Perl, Nick Berg, and others) in Jihadist videos
since 2002. Islamist and \quote{shock{}-site} web servers streamed these
videos across the internet using the low{}-bitrate Windows Media Video
codec, a proprietary variant of the industry{}-standard MPEG{}-4. The
shock of such events {--} the sight of a beheading, the sight of a
journalist pleading for her life {--} depends on its circulation
through online and broadcast media. A video beheading lies at the outer
limit of the ordinary visual pleasures and excitations attached to
video cultures. Would that beheading, a corporeal event that takes
video material culture to its limits, occur without codecs and
networked media?}

While images are visible, wireless signals are
relatively hard to sense. So they are a \quote{hard case} to analyse. We know
they surround us, but we hardly have any sensation of them. A tightly
packed labyrinth of digital signal processing lies between antenna and
what reaches the business travellers' eyes and ears. Much of what they
look at and listen has passed through wireless chipsets. The chipsets,
produced by Broadcom, Intel, Texas Instruments, Motorola, Airgo or
Pico, are tiny (1 cm) fragments that
support highly convoluted and concatenated paths on nanometre scales.
In wireless networks such as Wi{}-Fi, Bluetooth, and 3G mobile phones
with their billions of miniaturised chipsets, we encounter a vast
proliferation of relations. What is at stake in these convoluted,
compressed packages of relationality, these densely patterned
architectures dedicated to wireless communication? 

Take for instance the picoChip, a latest{}-generation wireless digital
signal processing chip, designed by a \quote{fabless} semiconductor company,
picoChip Designs Ltd, in Bath, UK. The product brief describes the chip
as:

\QuoteStyle{[t]he architecture of choice for next{}-generation wireless. Expressly
designed to address the new air{}-interfaces, picoChip's multi{}-core
DSP is the most powerful baseband processor on the market. Ideally
suited to WiMAX, HSPA, UMTS{}-LTE, 802.16m, 802.20 and others, the
picoArray delivers ten{}-times better MIPS/\$ than legacy approaches.
Crucially, the picoArray is easy to program, with a robust development
environment and fast learning curve. {\em (PicoChip, 2007)}} 

Written for electronics engineers, the key points here are that the chip
is designed for wireless communication or \quote{air{}-interface}, that its
purpose is to receive and transmit information wirelessly, and that it
accommodates a variety of wireless communication standards (WiMAX,
HSPA, 802.16m, etc). In this context, much of the terminology of
performance and low cost is familiar. The chip combines computing
performance and value for money (\quotation{ten times better MIPS/\$ {--}
Million Instructions Per Second/\$}) as a \quote{baseband processor}. That
means that it could find its way into many different version of
hardware being produced for applications that range between
large{}-scale wireless information infrastructures and small consumer
electronics applications. Only the last point is slightly surprisingly
emphatic: \quotation{[c]rucially, the picoArray is easy to program, with a robust
development environment and fast learning curve.} Why should ease of
programming be important?

\SubSubTitle{And why should so many processors be needed for
wireless signal processing?} 

The architecture of the picoChip stands on shifting ground. We are
witnessing, as Nigel Thrift writes, \quotation{a major change in the geography of
calculation. Whereas \quote{computing} used to consist of {\em centres
of calculation} located at definite sites, now, through the medium of
wireless, it is changing its shape} (Thrift, 2004, 182). The
picoChip's architecture is a respond to the changing
geographies of calculation. Calculation is not carried out at definite
sites, but at almost any site. We can see the picoChip as an {\em 
architectural} response to the changing {\em geography} of
computing. The architecture of the picoChip is typical in the ways that
it seeks to make a constant re{}-shaping of computation possible,
normal, affordable, accessible and programmable. This is particularly
evident in the parallel character of its architecture. Digital signal
processing requires massive parallellisation: more chips everywhere,
and chips that do more in parallel. The advanced architecture of the
picoChip is typical of the shape of things more generally: 

\QuoteStyle{[t]he picoArray{\trademark} is a tiled processor architecture in
which hundreds of processors are connected together using a
deterministic interconnect. The level of parallelism is relatively fine
grained with each processor having a small amount of local memory. ...
Multiple picoArrayTM devices may be connected together to form systems
containing thousands of processors using on{}-chip peripherals which
effectively extend the on{}-chip bus structure. {\em (Panesar, et al.,
2006, 324)}}

\PlaceImage{mackenzie5.jpg}{Typical contemporary wireless infrastructure DSP chip architecture PicoChip202}

The array of processors shown then, is a partial representation, an armature for a much more extensive diffusion of
processors in wireless digital signal processing: in wireless base
stations, 3G phones, mobile computing, local area networks, municipal,
community and domestic Wi{}-Fi network, in femtocells, picocells, in
backhaul, last{}-mile or first mile infrastructures.

\SubSubTitle{Architectures and intensive movement}

It is as if the picoChip is a miniaturised version of the urban
geography that contains the many gadgets, devices, and wireless and
wired infrastructures. However, this proliferation of processors is
more than a diffusion of the same. The interconnection between these
arrays of processors is not just extensive, as if space were blanketed
by an ever finer and wider grid of points occupied by processors at
work shaping signals. As we will see, the interconnection between
processors in DSP seeks to potentialise an {\em intensive movement}.
It tries to accommodate a change in the nature of movement. Since all
movement is change, intensive movement is a change in change. When
intensive movement occurs, there is always a change in kind, a
qualitative change.


Intensive movements always respond to a relational problem. The crux of
the relational problem of wirelessness is this: how can many things
(signals, messages, flows of information) occupy the same space at the
same time, yet all be individualised and separate? The flow of
information and messages promises something highly individualised (we
saw this in the UMPC video from Intel). In terms of this
individualising change, the movement of images, messages and data, and
the movement of people, have become linked in very specific ways today.
The greater the degree of individualization, the more dense becomes the
mobility of people and the signals they transmit and receive. And as
people mobilise, they drag personalised flows of communication on the
move with them. Hence flows of information multiply massively, and
networks must proliferate around those flows. The networks need to
become more dense, and imbricate lived spaces more closely in response
to individual mobility. 

This poses many problems for the architecture of communication
infrastructure. The infrastructural problems of putting networks
everywhere are increasingly, albeit only partially, solved by packing
radio{}-frequency waves with more and more intricately modulated signal
patterns. This is the core response of DSP to the changing geography of
calculation, and to the changing media embodiments associated with it.
To be clear on this: were it not for digital signal processing, the
problems of interference, of unrelated communications mixing together,
would be potentially insoluble. The very possibility of mobile devices
and mobility depends on ways of increasing the sheer density of
wireless transmissions. Radio spectrum becomes an increasingly
valuable, tightly controlled resource. For any one individual
communication, not much space or time can be available. And even when
there is space, it may be noisy and packed with other people and things
trying to communicate. Different kinds of wireless signals are
constantly added to the mix. Signals may have to work their way through
crowds of other signals to reach a desired receiver. Communication does
not take place in open, uncluttered space. It takes place in messy
configurations of buildings, things and people, which obstruct waves
and bounce signals around. The same signal may be received many times
through different echoes (\quote{multipath echo}). Because of the presence of
crowds of other signals, and the limited spectrum available for any one
transmission, wirelessness needs to be very careful in its selection of
paths if experience is to stream rather than just buzz. The problem for
wireless communication is to micro{}-differentiate many paths and to
allow them to interweave and entwine with each other without coming
into relation.

So the changing architectures of code and computation associated with
DSP in wireless networks does more, I would argue, than fit in with
changing geography of computing. It belongs to a more intensive,
enveloped, and enveloping set of movements. To begin addressing this
dynamic, we might say that wireless DSP is the armature of a
{\em centre of envelopment.} This is a concept that Gilles Deleuze
proposes late in {\em Difference and Repetition}.{\em } \quote{Centres
of envelopment} are a way of understanding how extensive movements
arise from intensive movement. Such centres crop up in \quote{complex
systems} when differences come into relation: 

\QuoteStyle{to the extent that every phenomenon finds its reason in a difference of
intensity which frames it, as though this constituted the boundaries
between which it flashes, we claim that complex systems increasingly
tend to interiorise their constitutive differences: the centres of
envelopment carry out this interiorisation of the individuating
factors. {\em (Deleuze, 2001, 256)}}

Much of what I have been describing as the intensive movement that folds
spaces and times inside DSP can be understood in terms of an
interiorisation of constitutive differences. An intensive movement
always entails a change in the nature of change. In this case, a
difference in intensity arises when many signals need to co{}-habit
that same place and moment. The problem is: how can many signals move
simultaneously without colliding, without interfering with each other?
How can many signals pass by each other without needing more space?
These problems induce the compression and folding of spaces inside
wireless processing, the folding that we might understand as a \quote{centre
of envelopment} in action.

\SubSubTitle{The Fast Fourier Transform: transformations between time and
space}

I have been arguing that the complications of the mathematics and the
convoluted nature of the code or hardware used in DSP, stems from an
intensive movement or constitutive difference that is interiorised. We
can trace this interiorisation in the DSP used in wireless networks. I
do not have time to show how this happens in detail, but hopefully one
example of DSP that occurs but in the video codecs and wireless
networks will illustrate how this happens in practice. 

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 \quote{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 waves
(sinusoids) of different frequencies and amplitudes. Some of these
sinusoids make more important contributions to overall shape of the
waveform than others. Added together again, these sine or cosine waves
should exactly re{}-constitute the original signal. Crucially, a
Fourier transform can turn something that varies over time (a signal)
into a set of simple components (sine or cosine waves) that do not vary
over time. Put more technically, it switches between \quote{time} and
\quote{frequency} domains. Something that changes in time, a signal, becomes
a set of distinct components that can be handled
separately.\footnote{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.}

In a way, this analysis of a
complex signal into simple static component signals means that DSP does
use the set{}-based approaches 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 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 number of sub{}-carriers signals (52 in IEEE
802.11a/g). It splits the data stream into dozens of separate signals
of slightly different frequency that together evenly use the whole
available radio spectrum. This is done in such a way that many
different transmitters can be transmitting at the same time, on the
same frequency, without interfering with each other. The advantage of
spreading a single high speed data stream across many signals
({\quote wideband}) is that each individual
signal can carry data at a much slower rate. Because the data is split
into 52 different signals, each signal can be much slower (1/50). That
means each bit of data can be spaced 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, {\em 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
transformation involves {\quote changes in
kind}. Data does not simply move through space. It
changes in kind in order to move through space, a space whose geography
is understood as too full of potential relations.

\SubSubTitle{Conclusion}

A couple of points in conclusion:

\startitemize[a]
\item The spectrum of different wireless{}-audiovisual devices competing
to do more or less the same thing, are all a {\em reproduction of
the same}. Extensive movement associated with wireless networks and
digital video occur in various forms. Firstly in the constant
enveloping of spaces by wireless signals, and secondly in the dense
population of wireless spectrum by competing, overlapping signals,
vying for market share in highly visible, well{}-advertised campaigns
to dominate spectrum while at the same time allowing for the presence
of many others. 
\item Actually, in various ways, wirelessness puts the very primacy of
extension as space{}-making in question. Signals seem to be able to
occupy the same space at the same time, something that should not
happen in space as usually understood. We can understand this by
re{}-conceptualising movement as intensive. Intensive movement occurs
in multiple ways. Here I have emphasised the constant folding inwards
or {\em interiorisation of heterogeneous movements} via
algorithms used in digital signal processing. Intensive movement ensues
occurs when a centre of envelopment begins to interiorise differences.
While these interiorised spaces are computationally intensive (as
exemplified by the picoChip's massive processing
power), the spaces they generate are not perceived as calculated,
precise or rigid. Wirelessness is a relatively invisible, messy,
amorphous, shifting sets of depths and distances that lacks the visible
form and organisation of other entities produced by centres of
calculation (for instance, the shape of a CAD{}-designed building or
car). However, similar processes occur around sound and images through
DSP. In fact, different layers of DSP are increasingly coupled in
wireless media devices.
\item Where does this leave the centre of envelopment? The cost of this
freeing up of movement, of mobility, seems to me to be an
interiorisation of constitutive differences, not just in DSP code but
in the perceptual fields and embodiment of the mobile user. The irony
of the DSP is that it uses code to quantify sensations or physical
movements that lie at the fringes of representation or awareness. We
can't see DSP as such, but it supports our seeing and
moving. {\em It brings code quite close to the body}. It can work
with audio and images in ways that bring them much closer to us. The
proliferation of mobile devices such as mp3 and digital cameras is one
consequence of that. Yet the price DSP pays for this proximity to
sensation, to sounds, movement, and others, is the envelopment I have
been describing. DSP acts as a centre of envelopment, as something that
tends to interiorise intensive movements, the changing nature of
change, the intensive movements that give rise to it. 
\item This brings us back to the UMPC video: it shows two individuals.
Their relation can never, it seems, get very far. The provision of
images, sound and wireless connectivity has come so far, that they
hardly need encounter each other at all. There is something intensely
monadological here: DSP is heavily engaged in furnishing the interior
walls of the monad, and with orienting the monad in relation to other
monads, but making sure that nothing much need pass between them. So
much has already been pre{}-processed between, that nothing much need
happen between. They already have a complete perception of their
relation to the other. 
\item On a final constructive note, it seems that there is room for
contestation here. The question is how to introduce the set{}-based
code processes that have proven productive in other areas into the
domain of DSP. What would that look like? How would it be sensed? What
could it do to our sensations of video or wireless media?
\stopitemize

\page

\SubSubTitle{References}

Deleuze, Gilles. {\em Difference and Repetition}. Translated by Paul Patton, {\em Athlone Contemporary European Thinkers}. (London; New
York: Continuum, 2001).

Panesar, Gajinder, Daniel Towner, Andrew Duller, Alan Gray, and Will Robbins. {\quote Deterministic Parallel Processing}, {\em International Journal of Parallel
Programming} 34, no. 4 (2006): 323{}-41.

PicoChip. 'Advanced Wireless Technologies', (2007). \Url{http://www.picochip.com/solutions/advanced_wireless_technologies}

PicoChip. 'Pc202 Integrated Baseband Processor Product Brief', (2007). 
\Url{http://www.picochip.com/downloads/03989ce88cdbebf5165e2f095a1cb1c8/PC202_product_brief.pdf}

Smith, Steven W. {\em The Scientist and Engineer's Guide to Digital Signal Processing}: California Technical Publishing, 2004).

Thrift, Nigel. {\quote Remembering the Technological Unconscious by Foregrounding Knowledges of Position}, {\em Environment \& Planning D: Society \& Space} 22, no. 1 (2004): 175{}-91.