Detection Theory: An Overview
Detection theory is a branch of applied mathematics and engineering that studies the detection and recognition of signals in noise. It is used in a variety of applications, including radar, radio communication, sonar, geophysical exploration, and medical imaging. Detection theory is heavily used in the field of signal processing, and its concepts are essential for understanding the performance of a wide range of detection and recognition systems. This article provides an overview of the fundamentals of detection theory, including its principles, applications, and limitations.
Principles
Detection theory is based on the principles of signal detection and recognition. The signal detection process involves recognizing the presence of a signal in the presence of noise. This is accomplished by measuring the signal-to-noise ratio (SNR) of the signal. The SNR measures the ratio of the signal power to the noise power.
In order to detect a signal, it must first be recognized. This is done by identifying the unique characteristics of the signal, such as its frequency, amplitude, or phase. Once the signal is recognized, it can be compared to a known reference signal. If the signal matches the reference, it is considered to be detected.
Applications
Detection theory is widely used in a variety of applications, including radar, radio communication, sonar, geophysical exploration, and medical imaging. In the field of radar, detection theory is used to detect and track objects in the air, sea, or space. In the field of radio communication, it is used to detect and classify signals. In the field of sonar, it is used to detect and identify underwater objects. In the field of geophysical exploration, it is used to detect and identify subsurface features. In the field of medical imaging, it is used to detect and identify abnormal tissue.
Limitations
Detection theory is limited by the SNR of the signal. If the SNR is too low, the signal may be too weak to be detected. Additionally, detection theory is limited by the accuracy of the reference signal used to recognize the signal. If the reference is inaccurate, the signal may not be correctly identified.
Conclusion
Detection theory is a branch of applied mathematics and engineering that studies the detection and recognition of signals in noise. It is used in a variety of applications, including radar, radio communication, sonar, geophysical exploration, and medical imaging. Detection theory is based on the principles of signal detection and recognition and is limited by the SNR of the signal and the accuracy of the reference signal.
References
Au, S. K. (2010). Detection Theory: Applications and Digital Signal Processing. New York, NY: John Wiley & Sons.
Kay, S. M. (1998). Fundamentals of Statistical Signal Processing: Detection Theory. Upper Saddle River, NJ: Prentice Hall.
Krantz, D. (2007). Detection Theory: A User’s Guide. Hoboken, NJ: John Wiley & Sons.
Leroy, P. (2005). Detection and Estimation Theory. Upper Saddle River, NJ: Prentice Hall.
Osborne, M. R. (2012). Detection Theory: An Introduction. London, UK: Routledge.