1.5. Application Areas
The statistical signal processing algorithms to be described find application in many fields. Some of these are:
- Communications - transmission and reception of digital information [Proakis and Salehi 2007]
- Radar and sonar - target detection, localization, and tracking [Richards 2005, Burdic 1984]
- Biomedicine - heart arrhythmia detection, brain computer interfaces [So¨rnmo and Laguna 2005, Sanei and Chambers 2007]
- Image processing - medical diagnostic imaging, data compression [Gonzalez and Woods 2008]
- Speech processing - speech recognition and synthesis [Rabiner and Schafer 2007]
- Radio navigation - global positioning systems [Pany 2010].
This is but a small sampling of applications with many more being added every day. At first glance it may seem strange that these somewhat diverse fields employ nearly the same statistical signal processing algorithms. This was not always so. This confluence of approaches is mainly due to the use of the modern digital computer for implementation of signal processing. Whether the signal is electrical, as in radar, acoustic, as in sonar and speech, or optical, as in imaging, it ultimately is reduced to a set of numbers to be input and stored within a digital computer. The transformation from a physical signal, say speech, to a set of numbers is accomplished via a transducer, say a microphone, followed by an A/D convertor to produce a set of bytes to be read and stored for further processing within a digital computer. The only difference from a signal processing perspective is the character of the signal. It can be lowpass, having most of its energy at low frequencies, as in speech, or bandpass, having its energy within a given band, as in a radar signal. It can be one-dimensional in nature, as in an acoustic signal, or two-dimensional, as in an image. The sampling rate of the A/D convertor will therefore need to be tailored to the signal under consideration and will result in different amounts of data to process. However, remarkably similar, if not identical, algorithms are used to process these widely disparate types of signals. Matched filters are used in sonar, where the signal spectrum has frequencies in the KHz range, but also in radar, where the signal spectrum has higher frequencies, usually in the GHz range. FFTs are used for one-dimensional signals such as speech, but also the two-dimensional version of the FFT is used for image analysis. As a result, it is not unusual to design signal processing algorithms based solely on a mathematical description of the signal and noise without reference to their origins. This would of course ignore any prior knowledge of the real-world constraints that the signal and noise must obey, and so any subsequent algorithm developed may have the potential for improved performance by imposing these constraints. Knowing, for example, that a signal evolved from a reflection from a moving target allows the radar designer to put a constraint on the Doppler frequency shift due to the constraint on maximum target speed.