Paul J. Nahin

A Simplified Derivation of Frei's Histogram Hyperbolization for Image Enhancement

Frei has recently introduced a new technique (histogram hyperbolization) for image enhancement by the manipulation of the picture brightness levels. An alternative derivation of Freis result, both simpler and more general, is presented.

The Laser BMD and Other Radiant Energy Weapons: Some Thoughts

This paper opens with a discussion of the ABM Treaty and the particular language in it that presently excludes the deployment of a laser BMD. Eight pressure points are then presented that may cause both the Soviets and the Americans to reevaluate the payoff of such ACD agreements to their overall national security, even to the extent of abrogating the Outer Space Treaty and SALT Phase I. Next an extended presentation of the current state of affairs in the American laser research program is given to show the magnitude of the U. S. commitment to developing radiant energy weapons technology. The paper concludes with a brief excursion into the psychological and strategic systems impact of laser weapons.

Communication with the Past

One way to communicate with the past is to ‘simply’ live backwards in time. Philosophers and other writers of speculative fiction were the first to wonder what things might be like in a world where the time asymmetry is reversed—that is, in a world where time ‘runs backward.’ Indeed, fascination with the idea of time reversal actually dates back thousands of years, long before science fiction, as it can be found in Plato’s dialogue Statesman, written (most probably) 15 years before Plato’s death in 347 B.C.

Among the giants: Oliver Heaviside: Genius and curmudgeon: He called establishment mathematicians `woodenheaded¿ when his powerful new methods perplexed them. His fellow EEs didn't know what to make of him either

Mention the innovators associated with telephony ¿ Alexander Graham Bell or Lord Kelvin, among others ¿ and one important name will probably not be included: Oliver Heaviside, Yet it was his formula for loading telephone lines to avoid signal distortion that made transatlantic communications possible. Heaviside used mathematics for his proofs; he left to others the task of building the hardware models, as well as the credit for his discoveries. Described by some as ¿an example of that genius which is akin to madness¿ and ¿a first-rate oddity,¿ this English intellect of the nineteenth century died, mostly unnoticed, in poverty.

Can Land-Based Strategic Bombers Survive an SLBM Attack?

The B-1 bomber will receive Presidential review in early 1977. A recent study by the Brookings Institution on the B-1 contains an erroneous analysis of its survivability in an SLBM attack, which detracts from the overall merit of the study. This issue is discussed and an alternative analysis is presented.

An error analysis of an algorithm for Marcum's Q-function

McGees iterative algorithm for calculating Marcums Q-Function is useful in many numerical studies in radar and communication systems. An analysis is presented that allows estimates on the computation time required, as a function of the desired accuracy, to support a call to a subroutine implementing this algorithm.

Basic Circuit Concepts

There are three fundamental components commonly used in electrical/electronic circuitry: resistors, capacitors, and inductors (although this last component will get some qualifying remarks in just a bit). Another component commonly encountered is the transformer and it will get some discussion, too, later. All of these components are passive. That is, they do not generate electrical energy, but either dissipate energy as heat (resistors) or temporarily store energy in an electric field (capacitors) or in a magnetic field (inductors). Transformers involve magnetic fields, as do inductors, but do not store energy. We’ll return to transformers later in the book. The first three components have two-terminals (the transformer in its simplest form has four), as shown in Fig. 1.1.

Transients in the Time Domain

The circuit in Fig. 2.1 has had the switch closed for a long time, and then it is opened (as shown) at time t = 0. What is the capacitor voltage vc (at point a) for time t ≥ 0? We could start to answer this question by writing down Kirchhoff’s equations and then doing some (maybe more than a little) algebra, but instead let’s see if we can use the ideas from Chap. 1 to arrive at the solution without doing a lot of algebra.

Transients in the Transform Domain

In this first example you’ll see the full power of the Laplace transform in doing a traditional transient analysis. (You’ll also experience its full grubbiness!) Figure 4.1 shows a circuit that is suddenly hit by a unit step voltage v(t) = u(t), and our problem is to determine the resulting voltage e(t). This circuit might, for example, be a simple model for a power station transformer connected (through the 30 μH inductor) to an overhead transmission line that has just been hit by a lightning stroke, a potentially catastrophic event (simply scale our final result up from our assumed one-volt surge to, say, a more realistic 100,000 volts). Determining e(t) would tell the transformer designers what sort of ‘safety-factor’ they should consider for the survival of the transformer when confronted by such a large voltage surge, both in terms of the magnitude and the duration of the surge.

The Laplace Transform

As you’ve seen in the first two chapters, the time domain analysis of electrical circuits results in equations containing time derivatives. Often a lot of derivatives. This doesn’t necessarily make progress impossible, but time derivatives do add significantly to the horrors of calculation. The Laplace transformation allows us to get rid of differentiations.