Digital Signal Processing Reference
In-Depth Information
Tabl e 1 .2
Uncompressed and compressed data rates.
Signal
Uncompressed Rate
Common Rate
l
g
r
,
y
i
d
.
,
©
,
L
s
Music
4.32 Mbit
/
s(CDaudio)
128 Kbit
/
s(MP3)
Voice
64 Kbit
/
s(AMradio)
4.8 Kbit
/
s (cellphone CELP)
Photos
14 MB (raw)
300 KB (JPEG)
Video
170 Mbit
/
s(PAL)
700 Kbit
/
s(DivX)
1.5 How to Read this Topic
This topic tries to build a largely self-contained development of digital sig-
nal processing theory
fromwithin discrete time
, while the relationship to the
analog model of the world is tackled only after all the fundamental “pieces
of the puzzle” are already in place. Historically, modern discrete-time pro-
cessing started to consolidate in the 50's when mainframe computers be-
came powerful enough to handle the effective simulations of analog elec-
tronic networks. By the end of the 70's the discipline had by all standards
reached maturity; so much so, in fact, that the major textbooks on the sub-
ject still in use today had basically already appeared by 1975. Because of its
ancillary origin with respect to the problems of that day, however, discrete-
time signal processing has long been presented as a tributary tomuch more
established disciplines such as Signals and Systems. While historically justi-
fiable, that approach is no longer tenable today for three fundamental rea-
sons: first, the pervasiveness of digital storage for data (from CDs to DVDs
to flash drives) implies that most devices today are designed for discrete-
time signals to start with; second, the trend in signal processing devices is
to move the analog-to-digital and digital-to-analog converters at the very
beginning and the very end of the processing chain so that even “classically
analog” operations such as modulation and demodulation are now done in
discrete-time; third, the availability of numerical packages like Matlab pro-
vides a testbed for signal processing experiments (both academically and
just for fun) which is far more accessible and widespread than an electron-
ics lab (not to mention affordable).
The idea therefore is to introduce discrete-time signals as a self-standing
entity (Chap. 2), much in the natural way of a temperature sequence or
a series of flood measurements, and then to remark that the mathemati-
cal structures used to describe discrete-time signals are one and the same
with the structures used to describe vector spaces (Chap. 3). Equipped with
the geometrical intuition afforded to us by the concept of vector space, we
