By Ronald L. Allen
Bargains a well-rounded, mathematical method of difficulties in sign interpretation utilizing the most recent time, frequency, and mixed-domain equipment * both beneficial as a reference, an updated overview, a studying software, and a source for sign research recommendations * offers a steady advent to the math in order that the fewer mathematically adept reader should not beaten with speedy not easy research * Covers Hilbert areas, complicated research, distributions, random indications, analog Fourier transforms, and extra
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Additional info for Signal Analysis: Time, Frequency, Scale, and Structure
But if we consider that the variation may occur along a north-to-south line as well, then the temperature depends upon a distance measure x as well: T(x, h). Finally, over an area with location coordinates (x, y), the air temperature is a continuous function of three variables T(x, y, h). When a signal has more than one independent variable, then it is a multidimensional signal. We usually think of an “image” as recording light intesity measurements of a scene, but multidimensional signals— especially those with two or three independent variables—are usually called images.
Hence, preliminary signal smoothing may once again be useful. Toward this end, we may also employ discrete derivative formulas that use more signal values: 1 x ′ ( n ) = ------ [ x ( n – 2 ) – 8x ( n – 1 ) + 8x ( n + 1 ) – x ( n + 2 ) ] . 4) Standard numerical analysis texts provide many alternatives . Among the problems at the chapter’s end are several edge detection applications. They weigh some of the alternatives for $ltering, threshold selection, and $nding extrema. 8). The upshot is that the signal analyst must tailor the discrete derivative methods to the data at hand.
Our subject, signal analysis, concentrates on the mathematical foundations, processing, and especially the intepretation of one-dimensional, single-valued signals. Generally, we may select a single channel of a multichannel signal for consideration; but we do not tackle problems speci$c to multichannel signal interpretation. Likewise, we do not delve deeply into image processing and analysis. Certain images do arise, so it turns out, in several important techniques for analyzing signals. Sometimes a daunting one-dimensional problem can be turned into a tractable two-dimensional task.
Signal Analysis: Time, Frequency, Scale, and Structure by Ronald L. Allen