Reviews for Methods in Electromagnetic Wave Propagation

The average rating for Methods in Electromagnetic Wave Propagation based on 2 reviews is 3 stars.

Review # 1 was written on 2010-03-23 00:00:00 Forest Neff Do yourself a favor and hit yourself in the face with a bat a few times instead. Inpenetrable, set-theoretical definitions team up with the occasional absurd assertion: a one-two punch that left me listless, confused, and --eventually-- thirsty. After wading through forty-something pages, I quit reading outright on the following charming paragraph: " Note the symmetry between the Fourier transform and its inverse. In terms of the interpretation of the Fourier transform in signal analysis, this symmetry does not appear to have a simple intuitive explanation; [1] there seems to be no a priori reason why the descriptions of a signal in the time domain and the frequency domain should be symmetrical. [2] Mathematically, the symmetry is based on the fact that R is selfdual as a locally compact Abelian group; see Katznelson (1976).[3]" [brackets mine] Wait a minute. [1] Frequency is distinguishable in time: f = 1/T Can you spot the inversion? It is a small wonder that it can be integrated, and differentiated, in time. Common, nonmathematical use of the words 'integrate' and 'differentiate' serve as well. [2] Of course not. There is no a priori reason for anything. Sit down and listen. Satisfy yourself however you see fit that sound does, or does not, exist in time. What quantities do you need to measure? You are uniquely responsible for writing f = 1/T. [3] Jesus. Mathematically, the symmetry is based on our ability to divide and measure, continuously and by discrete increments, in time. You need only the division operator and the Postulate of Eudoxus: "n" "n+1" <----> "1/n", "1/(n+1)". Does the author agree he is able to do these things, or not? In this book, the symmetry is based on the fact that he wrote f=1/T on the previous page. No need to call Nancy Drew. See The Greeks c.400 BC. Kaiser may be aiming at the differential equation (and not f= 1/T) with this comment, but abandoned with only the term "symmetry", I am left to my own devices. Who can read the minds of men? If we are speaking of the differential equation of wave motion, his assertion is equally silly. The 'symmetry' in question is the explicit assumption (which may be false) that the symmetry exists: 1) We assume sound is a disturbance, it propagates at a fixed speed in an elastic medium, the motion of medium, listener and source are small relative to the propagation speed..... Any solution to this problem must constrain time and position to a linear function (x = mt + b). These assumptions are generally true, for sound. 2) We assume the solution to the wave equation is cyclic: that for any interval in time (frequency), f(x) = f(x+2a). This is often expressed with a = π: f(e^x) = f( e^i2πx ) There is no such thing as a sound source or recording that is invariantly cyclic for any frequency, over distance and time. That signal propagation is nevertheless fundamentally cyclic is true. Untangling the boundary has no a priori reason but the signal in question. The assumption of symmetry is a practical one, it permits us to analyze signals in the spectral domain. Mathematically, this symmetry is based on the fact that we have asked a question which requires us to construct it, in order to answer. R can be self-dual and compact all day long and and all nonperiodic signal will still convert wrongly (as noise) into the spectral domain. However, ANY system which gives its value as a function of x and t, where x + ct = (some constant), has the desired properties. See D'Alembert, c.1750. In short, we have symmetry because we decided to have it; it is a tool we use to analyze signals, and descriptive of propagation. To the extent the tool accurately reflects an audio signal, it is true. Not surprisingly, signal recognition and error analysis tools all require us to tell them where the signal is, and where it isn't. Always. There is no a priori symmetry. The assumption is false, and extremely practical. Because WE can distinguish a signal. IN ALL SERIOUSNESS: I was deeply disappointed in this book. I agree intensely with the introduction by Gerald Kaiser. His reasons for writing this book demonstrate a dedication to knowledge and its transmission that are rarely met. Unfortunately, he expects the lay reader to meet him on the most arcane terms in mathematics: pure abstraction. To assess the knowledge for oneself requires an intimate knowledge of the Algebra being abstracted, and to have satisfied oneself of the validity of each new operator and manipulation. These are unfortunate terms upon which to base an introduction. The problem is deeper. The author appears to believe the abstractions ground the algebra itself. He believes that the "reason" a person can add and divide, lies in "compactness", Abelian groups, set theory... in the elements we have carefully constructed UPON arithmetic and Algebra. No one can decide for me whether or not I am able to enumerate, and whether or not I accept the rules of addition, multiplication.... There can be no reaching back down to lift arithmetic up from underneath. This is a logical circle, and it is sufficient to undo mathematics. In the text, the practical result is that everything runs the wrong way. You take something for granted for five straight pages, and then the author confesses, we were "doing that all along." Other times, he appears not to notice that he depends upon his conclusions in advance. The unsuspecting reader may stop outright, faced with arguments which presuppose their own result. From a practical perspective, Kaiser erases all the material necessary to understand what problem is being posed, how we have decided to solve it, and the relationship between signals and our assumption, under transformation. It is troubling to find such obvious errors of judgment and logic at the highest levels of mathematics. And, finally, if you wish to be understood, we have a common, universal mathematical language. It is called the Algebra. An Alternative Suggestion: All of the groundwork for signal analysis is plainly laid out, and easier to read, in beginning texts on partial differential equations, signal processing, vector analysis, and physics. Unfortunately, for the reader with a limited mathematical background, these are new and vast subjects. We are back to the beginning: how can this information be presented without requiring a degree in mathematics or the physical sciences? I cannot recommend more highly the following answer: www.khanacademy.org

Review # 2 was written on 2014-10-20 00:00:00 Chris Callen kjkjkjk