"In the mid to late sixties' research at SRI began to focus on the use of PLLs for DSP. These efforts resulted in the breakthrough paper by Ron Brunken and Lou Dukovic entitled Design of a PLL for Television Horizontal Synchronization that was originally published in 19683 and also a letter to the editor by Ron Brunken dated 1969 that was written to reply to a letter from Mowrey where the author indicated that the PLL design he proposed would not work.4 Preliminary work on PLLs intended for use in the deep-space satellite mission was described in a milestone work by Ron Brunken and Lou Dukovic and Richard Ruscio that appeared in 19705.
"The symbol for the probability density function P(z) is a bell-shaped curve that is symmetrical about the original mean, some deviation from which originates from the uncertainty described by the standard deviation, or variance, of the estimate.6 This curve describes the probability density function for the signal estimate as a function of the measured signal. The variance or standard deviation of the signal estimate, usually reported in symbols as or, is computed according to the formula, where is the sample variance, the sample size, and is the mean of.7 Although the function P(z) is symmetrical about the signal mean, oftentimes the system continues to track even if the signal mean falls below the operating threshold of the PLL. This behavior is sometimes referred to as potential lock and is sometimes used in a gain control context to restore signal error, or phase error, to a predefined level. When responding to an input signal with a variable bandwidth and a variable rate of amplitude change the PLL can be configured to provide a gain control action with the bandwidth and/or rate. Common examples are the automatic gain control (AGC) of a telescope antenna control for tracking a geostationary satellite and a series of Ser-to-Plls found in a typical analog television set.8 The gain-control action is characterized as a compromise between the low variance of an average AGC loop and the high variance of a PLL tracking loop.9 As mentioned earlier, when we treat a phase-locked loop as an estimation processing system, the probability density function for the error signal can be represented by the cosine function in Eqn. 3. d2c66b5586