By Marshall N. Rosenbluth
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Half the power at a given frequency is assigned to the positive frequency, half to the negative frequency. This has been done to remove extraneous factors of 2 from the Fourier transforms of eqs. 17). Some writers assign all the power to the positive frequencies, and their formulas differ from ours by factors of 2. When T is large enough, any frequency w will be close to at least one of the frequencies w n, and on the basis of eqs. 19) J o is—as in eq. 16)—equal to the Fourier transform of the autocovariance function f(t).
6. THE SYNTHESIS OF FILTERSt The design of a filter to meet given specifications is known as "synthesis", in contrast to "analysis", which determines the behavior of the filter once it has been defined. The most common method of specifying a filter to be synthesized is to give the amplitude or the phase of its transfer function Y(w); the two are not independent. The first step in synthesis, called the "approximation problem", is to find a rational function Y'(w) with poles in the region Im w > O that meets the specifications within prescribed tolerances.
20). This model provides an apt description of a kind of noise that sometimes interferes with radar reception and is called "clutter". It consists of reflections of each transmitted pulse from a large number of randomly distributed scatterers such as raindrops in the air or wavelets on the surface of the sea. The current from a vacuum tube has a component of a similar kind, for each time an electron crosses from cathode to plate, a pulse is induced in the external circuit. The electrons are emitted at random times, but the amplitudes of the pulses may not be random because each electron carries a fixed charge.