Average Fractional Frequency
The average fractional frequency is defined as
where the average is taken over observation time τ, the y(t) is the fractional frequency error at time t and τ is the observation time.
Since y(t) is the derivative of x(t) we can without loss of generality rewrite it as
Read more about this topic: Allan Variance, Supporting Definitions
Famous quotes containing the words average, fractional and/or frequency:
“But the whim we have of happiness is somewhat thus. By certain valuations, and averages, of our own striking, we come upon some sort of average terrestrial lot; this we fancy belongs to us by nature, and of indefeasible rights. It is simple payment of our wages, of our deserts; requires neither thanks nor complaint.... Foolish soul! What act of legislature was there that thou shouldst be happy? A little while ago thou hadst no right to be at all.”
—Thomas Carlyle (1795–1881)
“Hummingbird
stay for a fractional sharp
sweetness, and’s gone, can’t take
more than that.”
—Denise Levertov (b. 1923)
“The frequency of personal questions grows in direct proportion to your increasing girth. . . . No one would ask a man such a personally invasive question as “Is your wife having natural childbirth or is she planning to be knocked out?” But someone might ask that of you. No matter how much you wish for privacy, your pregnancy is a public event to which everyone feels invited.”
—Jean Marzollo (20th century)