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A fractional-n frequency synthesizer can be constructed using two integer dividers, a divide-by-N, and a divide-by-(N + 1) frequency divider. With a modulus controller, N is toggled between the two values so that the VCO alternates between one locked frequency and the other. The VCO stabilizes at a frequency that is the time average of the two ...
This allows the synthesis of frequencies that are N/M times the reference frequency. This can be accomplished in a different manner by periodically changing the integer value of an integer-N frequency divider, effectively resulting in a multiplier with both whole number and fractional component. Such a multiplier is called a fractional-N ...
The PLL is locked at 917.94 MHz (f o) with a channel spacing frequency of 30 kHz (f r). The total integer count, therefore, is 30,598. Dividing this by 128 (M) yields a quotient of 239 with a remainder of 6, N, and A, respectively.
Given a fractional cover, in which each set S i has weight w i, choose randomly the value of each 0–1 indicator variable x i to be 1 with probability w i × (ln n +1), and 0 otherwise. Then any element e j has probability less than 1/( e × n ) of remaining uncovered, so with constant probability all elements are covered.
Thus it will produce an output of 100 kHz for a count of 1, 200 kHz for a count of 2, 1 MHz for a count of 10 and so on. Note that only whole multiples of the reference frequency can be obtained with the simplest integer N dividers. Fractional N dividers are readily available. [20]
If n (the number of variables) is a fixed constant, then the feasibility problem can be solved in time polynomial in m and log V. This is trivial for the case n=1. The case n=2 was solved in 1981 by Herbert Scarf. [13] The general case was solved in 1983 by Hendrik Lenstra, combining ideas by László Lovász and Peter van Emde Boas. [14]
In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear ...
In mathematical optimization, fractional programming is a generalization of linear-fractional programming. The objective function in a fractional program is a ratio of two functions that are in general nonlinear. The ratio to be optimized often describes some kind of efficiency of a system.