1
Signals and Biomedical
Signal Processing
1.1 INTRODUCTION AND OVERVIEW
The most fundamental concept that is frequently used in this book is a “signal.”
It is imperative to clearly define this concept and to illustrate different types of
signals encountered in signal and image processing. In this chapter, different types
of signals are defined, and the fundamental concepts of signal transformation and
processing are presented while avoiding detailed mathematical formulations.
1.2 WHAT IS A “SIGNAL”?
The definition of a signal plays an important role in understanding the capabilities
of signal processing. We start this chapter with the definition of one-dimensional
(1-D) signals. A 1-D signal is an ordered sequence of numbers that describes the
trends and variations of a quantity. The consecutive measurements of a physical
quantity taken at different times create a typical signal encountered in science and
engineering. The order of the numbers in a signal is often determined by the order
of measurements (or events) in “time.” A sequence of body temperature recordings
collected in consecutive days forms an example of a 1-D signal in time. The characteristics of a signal lie in the order of the numbers as well as the amplitude of the
recorded numbers, and the main task of all signal processing tools is to analyze
the signal in order to extract important knowledge that may not be clearly visible
to the human eyes.
We have to emphasize the point that not all 1-D signals are necessarily ordered
in time. As an example, consider the signal formed by the recordings of the temperature simultaneously measured at different points along a metal rod where the
distance from one end of the rod defines the order of the sequence. In such a
signal, the points that are closer to the origin (one end of the metal rod) appear
earlier in the sequence, and, as a result, the concept that orders the sequence is
“distance in space” as opposed to time. However, due to abundance of time signals
in many areas of science, in the literature of signal processing, the word “time”
is often used to describe the axis that identifies order. In this book, without losing
the generality of the results or concepts, we use the concept of time as the ordering axis, knowing that, in some signals, time should be replaced by other concepts
such as space.
Many examples of biological 1-D signals are heavily used in medicine
and biology. Recording of the electrical activities of the heart muscles, called
3
Signals and Biomedical
Signal Processing
1.1 INTRODUCTION AND OVERVIEW
The most fundamental concept that is frequently used in this book is a “signal.”
It is imperative to clearly define this concept and to illustrate different types of
signals encountered in signal and image processing. In this chapter, different types
of signals are defined, and the fundamental concepts of signal transformation and
processing are presented while avoiding detailed mathematical formulations.
1.2 WHAT IS A “SIGNAL”?
The definition of a signal plays an important role in understanding the capabilities
of signal processing. We start this chapter with the definition of one-dimensional
(1-D) signals. A 1-D signal is an ordered sequence of numbers that describes the
trends and variations of a quantity. The consecutive measurements of a physical
quantity taken at different times create a typical signal encountered in science and
engineering. The order of the numbers in a signal is often determined by the order
of measurements (or events) in “time.” A sequence of body temperature recordings
collected in consecutive days forms an example of a 1-D signal in time. The characteristics of a signal lie in the order of the numbers as well as the amplitude of the
recorded numbers, and the main task of all signal processing tools is to analyze
the signal in order to extract important knowledge that may not be clearly visible
to the human eyes.
We have to emphasize the point that not all 1-D signals are necessarily ordered
in time. As an example, consider the signal formed by the recordings of the temperature simultaneously measured at different points along a metal rod where the
distance from one end of the rod defines the order of the sequence. In such a
signal, the points that are closer to the origin (one end of the metal rod) appear
earlier in the sequence, and, as a result, the concept that orders the sequence is
“distance in space” as opposed to time. However, due to abundance of time signals
in many areas of science, in the literature of signal processing, the word “time”
is often used to describe the axis that identifies order. In this book, without losing
the generality of the results or concepts, we use the concept of time as the ordering axis, knowing that, in some signals, time should be replaced by other concepts
such as space.
Many examples of biological 1-D signals are heavily used in medicine
and biology. Recording of the electrical activities of the heart muscles, called
3