17-08-2012, 04:00 PM
Biosignal and Biomedical Image Processing
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Series Introduction
Over the past 50 years, digital signal processing has evolved as a major engineering
discipline. The fields of signal processing have grown from the origin
of fast Fourier transform and digital filter design to statistical spectral analysis
and array processing, image, audio, and multimedia processing, and shaped developments
in high-performance VLSI signal processor design. Indeed, there
are few fields that enjoy so many applications—signal processing is everywhere
in our lives.
When one uses a cellular phone, the voice is compressed, coded, and
modulated using signal processing techniques. As a cruise missile winds along
hillsides searching for the target, the signal processor is busy processing the
images taken along the way. When we are watching a movie in HDTV, millions
of audio and video data are being sent to our homes and received with unbelievable
fidelity. When scientists compare DNA samples, fast pattern recognition
techniques are being used. On and on, one can see the impact of signal processing
in almost every engineering and scientific discipline.
Because of the immense importance of signal processing and the fastgrowing
demands of business and industry, this series on signal processing
serves to report up-to-date developments and advances in the field. The topics
of interest include but are not limited to the following:
• Signal theory and analysis
• Statistical signal processing
• Speech and audio processing
TEXTBOOK PROTOCOLS
In most early examples that feature MATLAB code, the code is presented in
full, while in the later examples some of the routine code (such as for plotting,
display, and labeling operation) is omitted. Nevertheless, I recommend that students
carefully label (and scale when appropriate) all graphs done in the problems.
Some effort has been made to use consistent notation as described in
Table 1. In general, lower-case letters n and k are used as data subscripts, and
capital letters, N and K are used to indicate the length (or maximum subscript
value) of a data set. In two-dimensional data sets, lower-case letters m and n
are used to indicate the row and column subscripts of an array, while capital
letters M and N are used to indicate vertical and horizontal dimensions, respectively.
The letter m is also used as the index of a variable produced by a transformation,
or as an index indicating a particular member of a family of related
functions.*
Filter Order
The slope of a filter’s attenuation curve is related to the complexity of the filter:
more complex filters have a steeper slope better approaching the ideal. In analog
filters, complexity is proportional to the number of energy storage elements in
the circuit (which could be either inductors or capacitors, but are generally capacitors
for practical reasons). Using standard circuit analysis, it can be shown
that each energy storage device leads to an additional order in the polynomial
of the denominator of the transfer function that describes the filter. (The denominator
of the transfer function is also referred to as the characteristic equation.)
As with any polynomial equation, the number of roots of this equation will
depend on the order of the equation; hence, filter complexity (i.e., the number
of energy storage devices) is equivalent to the number of roots in the denominator
of the Transfer Function. In electrical engineering, it has long been common
to call the roots of the denominator equation poles. Thus, the complexity of the
filter is also equivalent to the number of poles in the transfer function. For
example, a second-order or two-pole filter has a transfer function with a secondorder
polynomial in the denominator and would contain two independent energy
storage elements (very likely two capacitors).
ANALOG-TO-DIGITAL CONVERSION: BASIC CONCEPTS
The last analog element in a typical measurement system is the analog-to-digital
converter (ADC), Figure 1.1. As the name implies, this electronic component
converts an analog voltage to an equivalent digital number. In the process of
analog-to-digital conversion an analog or continuous waveform, x(t), is converted
into a discrete waveform, x(n), a function of real numbers that are defined
only at discrete integers, n. To convert a continuous waveform to digital format
requires slicing the signal in two ways: slicing in time and slicing in amplitude
(Figure 1.10).