ch11_randsig

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu HST.582J / 6.555J / 16.456J Biomedical Signal and Image Processing Spring 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . HST582J/6.555J/16.456J Biomedical Signal and Image Processing Spring 2007 Chapter 11- RANDOM SIGNALS: BASIC PROPERTIES c Bertrand Delgutte 1999 Introduction In the preceding chapters, we have assumed that signals can be completely specified as either discrete or continuous functions of time. Such complete mathematical specifications are rarely, if ever, available for signals recorded from living systems. Far more commonly, signals are characterized by a set of properties or features. For example, we might know that the EKG consists of more-or-less regular peaks not exceeding 100 mv in amplitude, or that speech has most of its energy below 10 kHz. Because such characterizations are incomplete, there will in general exist a large class, or ensemble of signals that share these properties. When an ensemble of signals characterized by certain properties is processed by a dynamic system such as a linear filter, response signals will form another ensemble characterized by a new set of properties. Our task here and in Chapter 12 will be to determine properties of the ensemble of response signals from knowledge of properties of the input ensemble and system characteristics. Alternatively, we will design systems such that the output signals have certain desired properties, given a set of input properties. While these tasks cannot be solved in general, when the known input properties are long-term time averages, and the system has special properties (such being linear or memoryless), it will be possible to specify certain time averages of the response signals. Signals described in terms of averages are called random signals, random processes, or stochastic processes. The term random is used because the waveforms of such signals are typically irreg- ular and complicated. This term does not necessarily imply that such signals are unpredictable. More often than not, it means that, for a specific purpose, only an appropriate set of averages needs to be known for a class of signals. For example, it might be possible to completely spec- ify a speech signal if we knew the motions of the articulators for all times, and such detailed information would be of great value to speech scientists. On the other hand, for an engineer who is designing a telecommunication system, knowledge of the long-term average spectrum of speech might suce. To give another example, the electrocardiogram might be predictable from the electrical potentials of every cardiac muscle fibers, but such knowledge would be too cumbersome for deciding whether a patient needs a pacemaker. Thus, it is perfectly appropriate to model the same signal as being random for one particular purpose, and as being deterministic (i.e. completely specified mathematically) for another purpose. In...
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ch11_randsig - MIT OpenCourseWare http://ocw.mit.edu...

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