4
Biomedical Signal and Image Processing
electrocardiogram (ECG), is widely considered as the main diagnostic signal in
assessment of the cardiovascular system. Electroencephalogram (EEG) is a signal
that records the electrical activities of the brain and is heavily used in diagnostics
of the central nervous system (CNS).
Multidimensional signals are simply extensions of the 1-D signals mentioned
earlier, i.e., a multidimensional signal is a multidimensional sequence of numbers
ordered in all dimensions. For example, an image is a two-dimensional (2-D)
sequence of data where numbers are ordered in both dimensions. In almost all
images, the numbers are ordered in space (for both dimensions). In a gray-scale
image, the value of the signal for a given set of coordinates (x, y), i.e., g(x, y), identifies the image brightness level at those coordinates. There are several important
types of image modalities that are heavily used for clinical diagnostics among
which magnetic resonance imaging (MRI), computed tomography (CT), ultrasonic images, and positron emission tomography (PET) are the most commonly
used ones. These imaging systems will be introduced in separate chapters dedicated to each image modality.
1.3 ANALOG, DISCRETE, AND DIGITAL SIGNALS
Based on the continuity of a signal in time and amplitude axes, the following three
types of signals can be recognized:
1.3.1 ANALOG SIGNALS
These signals are continuous both in time and amplitude. This means that both time
and amplitude axes are continuous axes and can take any real number. In other words,
at any given real values of time “t” the amplitude value “g(t)” can take any number
belonging to a continuous interval of real numbers. An example of such a signal is
the body temperature readings acquired using an analog mercury thermometer over
a certain period of time. In such a thermometer, the temperature is measured at all
times and the temperature value (i.e., the height of the mercury column) belongs to a
continuous interval of numbers. An example of such a signal is shown in Figure 1.1.
The signal illustrates the readings of the body temperature measured continuously
for 6000 s (or equivalently 100 min).
1.3.2 DISCRETE SIGNALS
In discrete signals, the amplitude axis is continuous but the time axis is discrete.
This means that, unlike in analog signals, the measurements of the quantity are
available only at certain specific times. In order to see why discrete signals are often
preferred over analog signals in many practical applications, consider the example
given earlier for analog signals. It is very unlikely that the body temperature may
change every second, or even every few minutes, and, therefore, in order to monitor
the temperature over a period of time, one can easily measure and sample the temperature only at certain times (as opposed to continuously monitoring the temperature as in the analog signal described earlier). The times at which the temperature
Biomedical Signal and Image Processing
electrocardiogram (ECG), is widely considered as the main diagnostic signal in
assessment of the cardiovascular system. Electroencephalogram (EEG) is a signal
that records the electrical activities of the brain and is heavily used in diagnostics
of the central nervous system (CNS).
Multidimensional signals are simply extensions of the 1-D signals mentioned
earlier, i.e., a multidimensional signal is a multidimensional sequence of numbers
ordered in all dimensions. For example, an image is a two-dimensional (2-D)
sequence of data where numbers are ordered in both dimensions. In almost all
images, the numbers are ordered in space (for both dimensions). In a gray-scale
image, the value of the signal for a given set of coordinates (x, y), i.e., g(x, y), identifies the image brightness level at those coordinates. There are several important
types of image modalities that are heavily used for clinical diagnostics among
which magnetic resonance imaging (MRI), computed tomography (CT), ultrasonic images, and positron emission tomography (PET) are the most commonly
used ones. These imaging systems will be introduced in separate chapters dedicated to each image modality.
1.3 ANALOG, DISCRETE, AND DIGITAL SIGNALS
Based on the continuity of a signal in time and amplitude axes, the following three
types of signals can be recognized:
1.3.1 ANALOG SIGNALS
These signals are continuous both in time and amplitude. This means that both time
and amplitude axes are continuous axes and can take any real number. In other words,
at any given real values of time “t” the amplitude value “g(t)” can take any number
belonging to a continuous interval of real numbers. An example of such a signal is
the body temperature readings acquired using an analog mercury thermometer over
a certain period of time. In such a thermometer, the temperature is measured at all
times and the temperature value (i.e., the height of the mercury column) belongs to a
continuous interval of numbers. An example of such a signal is shown in Figure 1.1.
The signal illustrates the readings of the body temperature measured continuously
for 6000 s (or equivalently 100 min).
1.3.2 DISCRETE SIGNALS
In discrete signals, the amplitude axis is continuous but the time axis is discrete.
This means that, unlike in analog signals, the measurements of the quantity are
available only at certain specific times. In order to see why discrete signals are often
preferred over analog signals in many practical applications, consider the example
given earlier for analog signals. It is very unlikely that the body temperature may
change every second, or even every few minutes, and, therefore, in order to monitor
the temperature over a period of time, one can easily measure and sample the temperature only at certain times (as opposed to continuously monitoring the temperature as in the analog signal described earlier). The times at which the temperature