 TE and TIE for the clock signals shown in Figure 5-15 are as follows (the measurement process starts at clock period n or (n)-th Tc): (n 1) (n 2) (n + k) Reference clock Measured clock X(n+ 1) X(n+ 2) X(n+ k) Figure 5-15 Time Error for k Cycle Periods as an Observation Interval TE at (n)-th T = difference between measured clock and reference = x(n) TE at (n + 1)-th T = difference between measured clock and reference = x(n+1) And similarly, TE at (n + k) th T = X(n+k) and SO on TIE for first observation interval (k cycles between N and N = To characterize the timing performance of a clock, the timing test device measures (observes) and records the TIE as the test proceeds (as the observation interval gets longer and longer). So, if the clock period (Tc) is 1 S, then the first observation interval after the start of the test will be at t = 1 S, then the second will be at t = 2 S, and SO on (assuming the observation interval steps are the same as the clock period). This way, TIE measures the total error that a clock has accumulated as compared to a reference clock since the beginning of the test. Also, because TIE is calculated from TE, TIE is also measured using units of seconds. For any measurement, by convention the value of TIE is defined to be zero at the start of the measurement. In comparison, the TE is the instantaneous measure between the two clocks; there is no interval be- ing observed. So, while the TE is the recorded error between the two clocks at any one instance, the TIE is the error accumulated over the interval (length) of an observation. Another way to think of it is that the TE is the relative time error between two clocks at a point (instant) of time, whereas TIE is the relative time error between two clocks accumulated between two points of time (which is an interval). Taking a simple example where the steps in the observation interval for a TIE measurement is the same as the period of a TE measurement, the TIE will exactly follow the contour of the TE. One case might be where the TE is being 