This paper addresses the frequency-domain characterization of stochastic signals in linear time-invariant distributed networks. A new general relation is derived. The average power flow at each frequency from one source to another through a lossless coupling network is shown to obey an inequality related to the second law of thermodynamics. The sources can be essentially any stationary random signal or noise processes; in particular, they need not represent thermal noise. In this sense the inequality is quite general. Proofs are based on standard techniques from the theory of linear circuits and random signals: thermodynamic concepts are used only for motivation and interpretation.
The development of pulse compression radar at MIT Lincoln Laboratory is related on the basis of the author's personal recollections. He describes the formation of the Radar Techniques Group, the development of the concept, the first system constructed, and the selection of an appropriate code for the transmitted waveform.< >
An integral equation for the pressure difference across the cochlear partition is derived from the classical assumptions. This equation can be solved to any desired precision by the numerical method of Lesser and Berkley. Alternately, making the usual long-wave assumption, it can be reduced to the second-order differential equation studied by Zwislocki and many others. Although many aspects of this solution agree with observations, the long-wave assumption is of doubtful validity for many interesting frequencies and locations, and the behavior is more sensitive to the size of the scalae than experimental results suggest. A third approach is to make the short-wave assumption proposed by Otto Ranke. The integral equation then can be transformed into a pair of first-order differential equations which can easily be solved in closed form. The resulting simple formulas can be fit to most of the observations of Békésy and others. In addition, the short-wave theory leads to simple explanations of “paradoxical motion” and the effects of bone conduction. The phase characteristics of the theory, however, show major deviations from the experiment—a failure which, it is believed, is due not to the short-wave approximation per se, but rather to the basic physical simplifications common to virtually all cochlear theories.
The MIT EECS Master of Engineering is a five-year program in electrical engineering and computer science, leading to the simultaneous award of bachelor's and master's degrees. The authors describe the new program from three different points of view. First, they authors describe the structure selected. Next they discuss the content of the curriculum. Finally, they report how the resources needed for the program have been estimated and secured.
In 1951, Harvey Fletcher published a comprehensive analysis of the macromechanical dynamic behavior of the cochlear partition in response to sound. Although not the first to derive the now-familiar one-dimensional long-wave differential equation, Fletcher’s discussion is so clear and so careful that it had considerable impact at the time and remains today a model of elegant biophysical thinking. His results, moreover, matched the observations then available (primarily those of von Bekesy). The last 44 years, however, have seen the introduction of a variety of new experimental observations casting serious doubts on whether the cochlea can usefully be considered a linear passive system as Fletcher and his contemporaries assumed. And new analytical tools, notably the wide availability of extensive computational facilities, have substantially altered our idea of what constitutes a workable mathematical model. This paper will review the place of models of the Fletcher type in our current understanding of cochlear behavior.
These twenty lectures have been developed and refined by Professor Siebert during the more than two decades he has been teaching introductory Signals and Systems courses at MIT. The lectures are designed to pursue a variety of goals in parallel: to familiarize students with the properties of a fundamental set of analytical tools; to show how these tools can be applied to help understand many important concepts and devices in modern communication and control engineering practice; to explore some of the mathematical issues behind the powers and limitations of these tools; and to begin the development of the vocabulary and grammar, common images and metaphors, of a general language of signal and system theory. Although broadly organized as a series of lectures, many more topics and examples (as well as a large set of unusual problems and laboratory exercises) are included in the book than would be presented orally. Extensive use is made throughout of knowledge acquired in early courses in elementary electrical and electronic circuits and differential equations. Contents Review of the "classical" formulation and solution of dynamic equations for simple electrical circuits • The unilateral Laplace transform and its applications • System functions • Poles and zeros • Interconnected systems and feedback • The dynamics of feedback systems • Discrete-time signals and linear difference equations • The unilateral Z-transform and its applications • The unit-sample response and discrete-time convolution • Convolutional representations of continuous-time systems • Impulses and the superposition integral • Frequency-domain methods for general LTI systems • Fourier series • Fourier transforms and Fourier's theorem • Sampling in time and frequency • Filters, real and ideal • Duration, rise-time and bandwidth relationships: The uncertainty principle • Bandpass operations and analog communication systems • Fourier transforms in discrete-time systems • Random Signals • Modern communication systems Circuits, Signals, and Systems is included in The MIT Press Series in Electrical Engineering and Computer Science, copublished with McGraw-Hill.
