Patent Publication Number: US-6990417-B2

Title: Jitter estimating apparatus and estimating method

Description:
The present patent application is a continuation application of PCT/JP01/02648 filed on Mar. 29, 2001 which is a continuation of U.S. patent application Ser. No. 09/538,135 filed on Mar. 29, 2000, now U.S. Pat. No. 6,460,001 the contents of which are incorporated herein by reference. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a jitter estimating apparatus and estimating method. 
   2. Description of the Related Art 
   A clock frequency of a microprocessor doubles every approximate 40 months. It is necessary to accurately measure jitter in a clock signal according to a shorter clock period. This is because a timing error is avoided in a system operation. 
   There are period jitter and timing jitter in jitter. For example, an operation frequency of a microprocessor in a computer is limited by period jitter in the clock signal in the microprocessor. Therefore, period jitter becomes a problem. Timing jitter becomes a problem as shift out of an ideal timing point in data communication. 
     FIGS. 1A to 1C  illustrate jitter in the clock signal. In the ideal clock signal which does not include jitter, since an interval T int  between a prescribed rise edge of the ideal clock signal and a rise edge adjacent to the prescribed rise edge is constant as shown with a wave of a dotted line in  FIG. 1A , period jitter is zero. A rise edge is wobbled before and after an arrow in an actual clock signal. Therefore, interval T int  is also wobbled with the wobbling of the rise edge. This wobbling becomes period jitter in the clock signal. Period jitter becomes a problem, for example, in the clock signal of the microprocessor in the computer. 
   As shown in  FIG. 1B , in a case where an ideal pulse signal without jitter is waveform of a broken line, an edge of a pulse signal with jitter (solid line) and the edge of the ideal pulse signal (broken line) is shifted. This shift width is timing jitter. 
   A time interval analyzer or an oscilloscope is used as means of measuring the jitter. They measure jitter by a method called as a zero cross method. 
     FIG. 2  illustrates a conventional jitter estimating apparatus using the time interval analyzer. In the conventional jitter estimating apparatus, the time interval analyzer  12  receives a clock signal (tested signal) x(t) output from a tested PLL (phase-locked loop)  11 . In the signal x(t), a next rise edge is wobbled against one rise edge as shown with a dotted line in  FIG. 2 . An interval Tp of both rise edges, that is, a period of the tested signal x(t) is wobbled. The time interval analyzer  12  measures a time interval between zero cross points of the signal x(t), that is, the period of the signal x(t). Histogram analysis for wobbling of the measured period is displayed. 
     FIG. 3  illustrates histogram of the period measured by the time interval analyzer. About the time interval analyzer, there is described in “Phase Digitizing Sharpens Timing Measurements”, by D. Chu (IEEE Spectrum, pp. 28–32, 1988), and “A Method of Serial Data Jitter Analysis Using One-Shot Time Interval Measurements” by J. Wilstrup (Proceeding of IEEE International Test Conference, pp. 819–823, 1998). 
     FIG. 4  illustrates a jitter estimating apparatus using a digital oscilloscope.  FIG. 5  illustrates components of the jitter estimating apparatus in the digital oscilloscope  14 .  FIGS. 6A and 6B  illustrate a tested signal and period jitter measured by the digital oscilloscope. 
   In recent years, a jitter estimating apparatus to measure jitter using an interpolation method is provided. A method of estimating jitter using the interpolation method (interpolation base jitter estimating method) is a method to measure timing of zero cross by interpolating between measured data close to zero cross in measured data of a sampled tested signal. That is, a time interval (period) between zero cross points is estimated by interpolating data and wobbling of the period is estimated. 
   The digital oscilloscope  14  receives the tested signal x(t) output from the tested PLL  11 . In the digital oscilloscope  14 , an A/D converter  15  converts the received tested signal x(t) into a digital signal. An interpolator  16  interpolates a signal value between values in which values of the digital signal is close to zero cross in the digital signal. 
   A period estimator  17  measures a time interval between zero cross and a histogram estimator  18  displays histogram of the measured value. An RMS and peak-to-peak detector  19  calculates a square mean and peak-to-peak value of wobbling of the measured time interval. In a case where the tested signal x(t) is a wave shown in  FIG. 6A , period jitter is measured as shown in  FIG. 6B . 
   It becomes a problem in an application of a computer for example whether or not the microprocessor normally operates even with a state where a worst value of period jitter in the clock signal of the microprocessor, an adjacent edge interval of the clock signal is maximum or minimum caused by the jitter. Based on this point, the quality of a microprocessor is judged by measuring the worst value, for example, of period jitter in the microprocessor and by judging whether or not the worst value is less than a prescribed value. 
   Especially, in a case of testing an electric device to generate a periodic signal such as a mass manufactured microprocessor, since it is necessary to measure jitter in a short time, the jitter estimating apparatus and the jitter estimating method capable of precisely measuring jitter in the short time are desired. 
   However, since there is dead time until next period measurement after a first period measurement in the conventional time interval analyzer, it takes time to obtain the number of data needed for histogram analysis. The digital oscilloscope cannot estimate histogram of jitter correctly and therefore jitter is over-evaluated. 
   SUMMARY OF THE INVENTION 
   Therefore, it is an object of the present invention to overcome these drawbacks in the prior art. 
   This object is achieved by combinations described in the independent claims. The dependent claims define further advantageous and exemplary combinations of the present invention. 
   In order to achieve the object, according to a first aspect of the present invention, there is provided a jitter estimating apparatus for estimating jitter of an input signal, which includes a phase noise detecting unit for calculating phase noise waveform of the input signal, and a worst value estimating unit for calculating a worst value of jitter of the input signal based on phase noise waveform. 
   It is preferable that the worst value estimating unit includes an absolute value calculator for calculating an absolute value of the phase noise waveform, a maximum value calculator for calculating a maximum value of the absolute value; and a constant multiplication unit for calculating multiplied value as the worst value multiplying the maximum value by constant. 
   The constant multiplication unit may include a means for calculating the worst value of a peak value of jitter in the input signal by approximately double the maximum value. 
   It is preferable that a jitter estimating apparatus further includes a timing jitter estimating unit for calculating timing jitter sequence of the input signal based on the phase noise waveform, a period jitter estimating unit for calculating period jitter sequence of the input signal based on timing jitter sequence; an RMS detecting unit for calculating a square mean of period jitter sequence; and a probability calculator for calculating probability in which a worst value of the peak value is generated based on the square mean and the worst value of the peak value. 
   The constant multiplication unit may include a means for calculating a worst value of a peak-to-peak value of jitter in the input signal by approximately quadruple the maximum value. 
   A jitter estimating apparatus may further include a timing jitter estimating unit for calculating timing jitter sequence of the input signal based on the phase noise waveform, a period jitter estimating unit for calculating period jitter sequence of the input signal based on timing jitter sequence, an RMS detecting unit for calculating a square mean of the period jitter sequence, and a probability calculator for calculating probability in which a worst value of the peak-to-peak value is generated based on the square mean and the worst value of the peak-to-peak value. 
   According to the second aspect of the present invention, there is provided a jitter estimating apparatus for estimating jitter of an input signal, which includes a phase noise detecting unit for calculating phase noise waveform of the input signal, and a probability estimating unit for calculating probability in which peak jitter and/or peak-to-peak jitter of the input signal are/is generated. 
   It is preferable that a jitter estimating apparatus further includes a timing jitter estimating unit for calculating timing jitter sequence of the input signal based on the phase noise waveform, in which the probability estimating unit detects probability in which peak jitter and/or peak-to-peak jitter of the input signal are/is generated based on the timing jitter sequence. 
   It is preferable that a jitter estimating apparatus further includes a low frequency component remover for removing a frequency component lower than a prescribed frequency from the phase noise waveform, in which the timing jitter estimating unit calculates timing jitter sequence of the input signal based on the phase noise waveform from which the frequency component is removed. 
   It is preferable that the probability estimating unit includes an RMS detecting unit for calculating a square mean of the phase noise waveform, and a probability calculator for calculating probability in which peak jitter or peak-to-peak jitter of the input signal exceeds a prescribed value based on the square mean. 
   The probability estimating unit may further include means for calculating a prescribed value by multiplying the square mean by constant. 
   The probability estimating unit may include an RMS detecting unit for calculating a square mean of the phase noise waveform, a peak-to-peak detecting unit for calculating a peak value and/or the peak-to-peak value of the timing jitter of the input signal based on the phase noise waveform; and a probability calculator for calculating probability in which peak jitter or peak-to-peak jitter of the input signal exceeds the peak value or the peak-to-peak value. 
   It is preferable that the phase noise detecting unit includes an analytic signal converting unit for converting the input signal into an analytic signal of a complex function, an instantaneous phase estimating unit for calculating an instantaneous phase of the analytic signal, and a linear phase remover for calculating the phase noise waveform by removing a linear phase from the instantaneous phase. 
   The phase noise detecting unit includes: an analytic signal converting unit for converting the input signal into an analytic signal of a complex function; an instantaneous phase estimating unit for calculating an instantaneous phase of the analytic signal; and a linear phase remover for calculating the phase noise waveform by removing a linear phase from the instantaneous phase. 
   A jitter estimating apparatus may further include a waveform clipper for removing an amplitude modulating component of the input signal, in which the analytic signal converting unit converts the input signal from which the amplitude modulating component is removed into the analytic signal. 
   It is preferable that a zero cross detecting unit outputs timing in which the analytic signal is sampled and data near a zero cross point among data of the sampled analytic signal are sampled, and the timing jitter estimating unit calculates timing jitter sequence of the input signal by sampling the phase noise waveform based on the timing. 
   A jitter estimating apparatus may further include a period jitter estimating unit for calculating period jitter sequence of the input signal based on timing jitter sequence, in which the probability estimating unit calculates probability in which a peak value and/or a peak-to-peak value of period jitter of the input signal exceeds a prescribed value based on the period jitter sequence. 
   A jitter estimating apparatus further includes a period jitter estimating unit for calculating period jitter sequence of the input signal based on timing jitter sequence, in which the stochastic probability estimating unit calculates stochastic probability in which a peak value and/or a peak-to-peak value of period jitter of the input signal exceeds a prescribed value based on the period jitter sequence. 
   It is preferable that the period jitter estimating unit includes a difference calculator for calculating difference sequence between timing jitter included in timing jitter output by the timing jitter estimating unit, an interval calculator for calculating an interval of the timing output by the zero cross detecting unit, and a correcting unit for calculating period jitter sequence by correcting the difference sequence based on the interval of the timing and a period of the input signal. 
   It is preferable that the period jitter estimating unit further includes a delay unit for delaying period jitter sequence calculated by the correcting unit to output the delayed sequence. 
   A jitter estimating apparatus may further include a cycle-to-cycle period jitter estimating unit for calculating cycle-to-cycle period jitter of the input signal based on the period jitter sequence, in which the probability estimating unit calculates probability in which a peak value and/or a peak-to-peak value of cycle-to-cycle period jitter of the input signal exceeds a prescribed value based on cycle-to-cycle period jitter sequence. 
   A jitter estimating apparatus may further include a switch for switching any of the linear phase remover, the timing jitter estimating unit, the period jitter estimating unit, and the cycle-to-cycle period jitter estimating unit connected to the probability estimating unit. 
   According to the third aspect of the present invention, there is provided a method of estimating jitter of an input signal, which includes steps of detecting phase noise to calculate phase noise waveform of the input signal, and estimating a worst value to calculate the worst value of jitter in the input signal based on the phase noise waveform. 
   It is preferable that the step of estimating the worst value includes steps of calculating an absolute value of the phase noise waveform, calculating a maximum value of an absolute value, and multiplying the maximum value by constant to calculate the multiplied value as the worst value. 
   The step of multiplying the maximum value by constant may have a step of calculating the worst value of a peak value in the input signal by approximately double the maximum value. 
   It is preferable that a method of estimating jitter, further includes steps of calculating timing jitter sequence of the input signal based on the phase noise waveform, calculating period jitter sequence of the input signal based on the timing jitter sequence, calculating a square mean of the period jitter sequence, and calculating probability in which a worst value of the peak value is generated based on the square mean and the worst value of the peak value. 
   The step of multiplying the maximum value by constant may include the step of calculating the worst value of a peak-to-peak value of jitter in the input signal by approximately quadruple the maximum value. 
   A method of estimating jitter may further include steps of calculating timing jitter sequence of the input signal based on the phase noise waveform, calculating period jitter sequence of the input signal based on the timing jitter sequence, calculating a square mean of the period jitter sequence, and calculating probability in which the worst value of the peak-to-peak value is generated based on the square mean and the worst value of the peak-to-peak value. 
   According to the third aspect of the present invention, there is provided a method of estimating jitter for estimating jitter of an input signal, which includes steps of detecting phase noise for calculating phase noise waveform of the input signal, and estimating probability for calculating probability in which peak jitter and/or peak-to-peak jitter of the input signal are/is generated based on the phase noise waveform. 
   It is preferable that a method of estimating jitter further includes a step of estimating timing jitter for calculating timing jitter sequence of the input signal based on the phase noise waveform, in which the step of estimating probability estimates probability in which peak jitter and/or peak-to-peak jitter of the input signal are/is generated based on the timing jitter sequence. 
   A method of estimating jitter may further include a step of removing a frequency component lower than a prescribed frequency from the phase noise waveform, in which the step of estimating timing jitter calculates timing jitter sequence of the input signal based on the phase noise waveform from which the frequency component is removed. 
   It is preferable that the step of estimating probability includes steps of calculating a square mean of the phase noise waveform, and calculating probability in which peak jitter or peak-to-peak jitter of the input signal exceeds a prescribed value based on the square mean. 
   The step of estimating probability may further include a step of calculating a prescribed value by multiplying the square mean by constant. 
   The step of estimating probability may include steps of: calculating a square mean of the phase noise waveform, detecting a peak-to-peak to calculate a peak value and/or a peak-to-peak value of timing jitter in the input signal based on the phase noise waveform, and calculating probability in which peak jitter or peak-to-peak jitter of the input signal exceeds the peak value or the peak-to-peak value based on the square mean, and the peak value or the peak-to-peak value. 
   It is preferable that the step of detecting phase noise includes steps of: converting an analytic signal to convert the input signal into the analytic signal of a complex function; calculating an instantaneous phase of the analytic signal; and removing a linear phase to calculate the phase noise waveform by removing a linear phase from the instantaneous phase. 
   The step of detecting phase noise includes steps of: converting an analytic signal to convert the input signal into the analytic signal of a complex function; calculating an instantaneous phase of the analytic signal; and removing a linear phase to calculate the phase noise waveform by removing a linear phase from the instantaneous phase. 
   A method of estimating jitter may further include a step of removing an amplitude modulating component of the input signal, in which the step of converting the analytic signal converts the input signal from which the amplitude modulating component is removed into the analytic signal. 
   It is preferable that a method of estimating jitter further includes a step of sampling the analytic signal to output timing in which data near a zero cross point among data of the analytic signal are sampled, in which the step of estimating timing jitter calculates timing jitter sequence of the input signal by sampling the phase noise waveform based on the timing. 
   A method of estimating jitter may further include a step of estimating period jitter to calculate period jitter sequence of the input signal based on the timing jitter sequence, in which the step of estimating probability calculates probability in which a peak value and/or peak-to-peak value of period jitter in the input signal exceeds a prescribed value based on the period jitter sequence. 
   A method of estimating jitter further includes a step of estimating period jitter to calculate period jitter sequence of the input signal based on the timing jitter sequence, in which the step of estimating stochastic probability calculates stochastic probability in which a peak value and/or peak-to-peak value of period jitter in the input signal exceeds a prescribed value. 
   It is preferable that the step of estimating period jitter includes steps of calculating difference sequence of timing jitter included in timing jitter sequence output in the step of estimating timing jitter, calculating an interval of timing output in the step of detecting the zero cross point, and calculating the period jitter sequence by correcting the difference sequence based on the interval of the timing and a period of the input signal. 
   It is preferable that the step of estimating period jitter further includes a step of delaying the period jitter sequence calculated in the correcting step to output the delayed sequence. 
   A method of estimating jitter may further include a step of estimating cycle-to-cycle period jitter to calculate cycle-to-cycle period jitter in the input signal based on the period jitter sequence, in which the step of estimating probability calculates probability in which a peak value and/or peak-to-peak value of cycle-to-cycle period jitter in the input signal exceeds a prescribed value based on the cycle-to-cycle period jitter sequence. 
   This summary of the invention does not necessarily describe all necessary features so that the invention may also be a sub-combination of these described features. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
     The above and other objects and features of the invention will become more apparent from the following detailed description of the preferred embodiments with reference to the attached drawings, wherein: 
       FIGS. 1A to 1C  illustrate jitter in a clock signal; 
       FIG. 2  illustrates a conventional jitter estimating apparatus using a time interval analyzer; 
       FIG. 3  illustrates histogram of a period measured by the time interval analyzer; 
       FIG. 4  illustrates a jitter estimating apparatus using a digital oscilloscope; 
       FIG. 5  illustrates components of the jitter measuring apparatus in the digital oscilloscope  14 ; 
       FIGS. 6A and 6B  illustrate a tested signal and period jitter measured by the digital oscilloscope; 
       FIGS. 7A and 7B  illustrate power spectrum obtained by performing high-speed Fourier transformation for the clock signal of a microprocessor in a computer; 
       FIGS. 8A and 8B  illustrate histogram (probability density function) of jitter in the clock signal (clock jitter) J[n]; 
       FIG. 9  illustrates Rayleigh probability density function; 
       FIG. 10  illustrates probability in which J p  is higher than a value of Ĵ pk ; 
       FIG. 11  illustrates one example of a jitter estimating apparatus according to one embodiment in the present invention; 
       FIG. 12  illustrates an RMS value J RMS  and a peak-to-peak value J pp  of period jitter of a tested signal having sine wave jitter; 
       FIGS. 13A and 13B  illustrate histogram of period jitter; 
       FIG. 14  illustrates the number of events, the RMS value of the period jitter, and the peak-to-peak value of period jitter; 
       FIG. 15  illustrates another example of the jitter estimating apparatus in the present invention; 
       FIGS. 16A to 16C  illustrate a real number part x c (t), phase noise wave Δφ(t), and period jitter J p (t) of an analytic signal z c (t); 
       FIG. 17  illustrates components of a period jitter estimating unit  51 ; 
       FIGS. 18A and 18B  illustrate relation of peak-to-peak value Δφ pp  of timing jitter Δφ in the clock signal (tested signal), output by the microprocessor, measured with the jitter estimating apparatus in the present invention, to the number of events; 
       FIGS. 19A and 19B  illustrate relation of peak-to-peak value J pp  of period jitter J p  in the clock signal (tested signal) output by the microprocessor, measured with the jitter estimating apparatus in the present invention, to the number of events; 
       FIGS. 20A and 20B  illustrate relation of peak-to-peak value J cc,pp  of cycle-to-cycle period jitter J cc  in the clock signal (tested signal), output by the microprocessor, measured with the jitter estimating apparatus in the present invention, to the number of events; 
       FIG. 21  illustrates the number of zero cross points needed for estimating a peak value of period jitter; 
       FIG. 22  illustrates measured values of jitter measured by the time interval analyzer and a Δφ method; 
       FIG. 23  illustrates another embodiment of the jitter estimating apparatus in the present invention; 
       FIG. 24  illustrates one example of an analytic signal converting unit  23 ; 
       FIG. 25  illustrates another example of the analytic signal converting unit  23 ; 
       FIG. 26  illustrates another example of the analytic signal converting unit  23 ; 
       FIG. 27  is a flowchart showing one example of the jitter estimating method in the present invention; 
       FIG. 28  illustrates a flowchart showing another example of the jitter estimating method; 
       FIG. 29  illustrates another example of a linear phase remover  27 ; and 
       FIG. 30  illustrates one part of a flowchart of the jitter estimating method of measuring jitter using the linear phase remover  27  in  FIG. 29 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Below, one example of an embodiment in the present invention will be described referring to drawings. 
   A principle of the present invention is described. In case where instantaneous value J[n] depends on the Gaussian distribution in an irregular process of narrow bandwidth {J(n)}, set value {max(J[n])} of a maximum value of J[n] comes close to Rayleigh distribution when free level n (the number of samplings) is great. 
     FIG. 7A  illustrates a power spectrum in a quiescent mode of a microprocessor, that is, in an inert state of the microprocessor, in the power spectrum by performing a high-speed Fourier transformation for a clock signal of a microprocessor in a computer. The inert state is a state, for example, where the computer awaits an instruction from a user and a state where in a microprocessor, only PLL circuit, which outputs the clock signal by supply of a phase reference with a reference clock, operates and the clock signal is seldom influenced from another unit of the computer. 
     FIG. 7B  illustrates a power spectrum in a noisy mode of the microprocessor, that is, in a state where the microprocessor is active. The activation state is a state, for example, where a memory of level  2 , a system bus, a core bus, a branch predicting unit, and the like fully operate in the computer and the clock signal is greatly influenced from another unit of the computer. 
   In  FIGS. 7A and 7B , line spectrum of the clock signal appears at 400 MHz, which is a fundamental frequency of the clock signal. Irregular phase noise occurs in a vicinity frequency band of a center frequency around 400 MHz. This shows appearance of narrow bandwidth irregular data. 
     FIG. 8A  illustrates a probability density function (histogram) of jitter in clock signal (clock jitter) J[n] in the quiescent mode of the microprocessor and  FIG. 8B  illustrates histogram of clock jitter J[n] in a noisy mode of the microprocessor. The probability density function of clock jitter J[n] is accordance with Gaussian distribution. 
   A set {J p }, which is {max(J[n])}, of a peak value of period jitter (peak jitter) in the clock signal is in accordance with Rayleigh distribution from a view point of irregular phase noise, instantaneous value J[n] of clock jitter, according to Gaussian distribution. 
   Probability density function P r (J p ) of Rayleigh distribution is obtained by the following formula. 
                       P   r     ⁡     (     J   p     )       =       ⁢           J   p       σ   J   2       ⁢     exp   ⁡     (     -       J   p   2       2   ⁢     σ   p   2           )       ⁢           ⁢     J   p       &gt;   0                 =       ⁢       0   ⁢           ⁢     J   p       &lt;   0                   (   1   )             
 
(where σ J  is a root mean square (RMS) value of clock jitter J[n] and σ J   2  is decentralization.)  FIG. 9  illustrates a Rayleigh probability density function. In case of J p  is over 0 (J p &gt;0), the Rayleigh probability density function satisfies relation of P r (J p ) is not equal to 0 (P r (J p )≠0), as shown in  FIG. 9 .
 
   When peak value J p  is in accordance with Rayleigh distribution, probability where J p  becomes higher than a value of Ĵ pk is obtained by the following formula. 
               P   ⁡     (       J   p     &gt;       J   ^       p   ⁢           ⁢   k         )       =         ∫       j   ^       p   ⁢           ⁢   k       ∞     ⁢       P   ⁡     (     J   p     )       ⁢           ⁢     ⅆ     J   p           =     exp   ⁡     (     -         J   ^       p   ⁢           ⁢   k     2       2   ⁢     σ   J   2           )                 (   2   )             
 
Standard deviation of Ĵ pk  is obtained by the following formula. 
               σ     J     p   ⁢           ⁢   k         =           4   -   π     2       ⁢     σ   J               (   2.1   )             
 
     FIG. 10  illustrates probability where J p  is higher than a value of Ĵ pk . 
   If Ĵ pk  is set as a worst value of period jitter and root mean σ J   2  of period jitter of a tested signal is measured, probability where period jitter of the tested signal exceeds worst value Ĵ pk  can be estimated. And it can be estimated that the smaller the probability is, the higher the reliability of a production process becomes. 
   Relation shown in a formula (2) can be applied for not only period jitter but also timing jitter and cycle-to-cycle period jitter for example. Cycle-to-cycle period jitter J cc [n] is obtained, for example, based on a difference of period jitter shown by the following formula.
 
 J   cc   [n]=J[n +1 ]−J[n]   (3)
 
When the probability density function of J[n] shows Gaussian distribution, 
                 P   r     ⁡     (   J   )       =       1     σ   ⁢       2   ⁢   π           ⁢     exp   ⁡     (     -       J   2       2   ⁢     σ   2           )                 (   4   )             
 
the probability density function of J cc  is given by its convolution. 
                 P   r     ⁡     (     J   cc     )       =       ∫     -   ∞     ∞     ⁢         1     σ   ⁢       2   ⁢   π             ⁢     exp   ⁡     (     -       x   2       2   ⁢     σ   2           )       ⁢     exp   ⁡     (     -         (     t   -   x     )     2       2   ⁢     σ   2           )       ⁢           ⁢     ⅆ   x                 (   5   )             
 
The probability density function of J cc  becomes Gaussian distribution as shown in the following formula based on center limit theorem. 
                   P   r     ⁡     (     J   cc     )       =         1     2   ⁢   σ   ⁢     π         ⁢     exp   ⁡     (     -       t   2       4   ⁢     σ   2           )         =       1       σ   ^     ⁢       2   ⁢   π           ⁢     exp   ⁡     (     -       Jcc   2       2   ⁢       σ   ^     2           )             ⁢           ,     
     ⁢       σ   ^     =       2   ⁢   σ                 (   6   )             
 
Cycle-to-cycle period jitter J cc [n] is a Gaussian random process and its peak value is in accordance with Rayleigh distribution.
 
   Generally, timing jitter is also the Gaussian random process and the peak value of timing jitter is in accordance with Rayleigh distribution. If a low frequency component of timing jitter is excluded, the probability density function of timing jitter closes to Gaussian distribution and hereby estimating precision of probability can be improved. 
   In  FIG. 1B , in a case where a rise edge of the clock signal at time  0  rises farthest from an ideal rise point, and then a rise edge of the clock signal at time T delays farthest from the ideal rise point to rise, that is, in a case where timing jitter Δφ( 0 ) of rise edge at time  0  is a maximum value at the negative side, −Δφmax, and timing jitter Δφ(T) of rise edge at time T is a maximum value at the positive side, +Δφmax, period jitter is a worst peak value in a positive direction.
 
 J′   p   + =Δφ max −(−Δφ max )=2Δφ max   (7)
 
   As shown in  FIG. 1C , in a case where timing jitter Δφ( 0 ) of rise edge of the clock signal at time  0  is the maximum value at the positive side, −Δφmax, and timing jitter Δφ(T) of rise edge of the clock signal at time T is a maximum value at the positive side, +Δφmax, period jitter is the worst peak value in a negative direction.
 
 J′   p   − =−Δφ max −Δφ max =−2Δφ max   (8)
 
The maximum value of the peak-to-peak of period jitter, worst value J′ pp  of period jitter in the clock signal is obtained by the following formula.
 
 J′   pp   =J′   p   +   −J′   p   − =4Δφ max   (9)
 
An absolute value of a maximum value in the positive direction and an absolute value of a maximum value in a negative direction of timing jitters are generally equal.
 
   When probability where peak value J p  of jitter in the tested signal exceeds Ĵ p  is given by the formula (2), probability where peak-to-peak value J pp  of jitter of the tested signal exceeds Ĵ pp  is obtained based on multiplication of probability where positive peak value J p   +  exceeds +Ĵ pp /2 by probability where negative peak value J p   −  exceeds −Ĵ pp /2. 
                       P   r     ⁡     (       J   pp     &gt;       J   ^     pp       )       =       ⁢         P   r     ⁡     (       J   p   +     &gt;     +         J   ^     pp     2         )       ·       P   r     ⁡     (       J   p   -     &gt;     -         J   ^     pp     2         )                     =       ⁢         P   r     ⁡     (       J   p   +     &gt;         J   ^     pp     2       )       ·       P   r     ⁡     (       J   p   -     &gt;         J   ^     pp     2       )                     =       ⁢       exp   ⁡     (     -         J   ^     pp   2       8   ⁢     σ   J   2           )       ⁢     exp   ⁡     (     -         J   ^     pp   2       8   ⁢     σ   J   2           )                     =       ⁢     exp   ⁡     (     -         J   ^     pp   2       4   ⁢     σ   J   2           )                     (   10   )             
 
   An embodiment of the present invention to measure jitter based on the above description will be described referring to an example. 
     FIG. 11  illustrates one example of a jitter estimating apparatus according to one embodiment in the present invention. A jitter estimating apparatus provides analytic signal converting unit  23 , instantaneous phase estimating unit  26 , linear phase remover  27 , zero cross sampler  43 , peak-to-peak detecting unit  32 , and square mean detecting unit  33 . 
   A/D converting unit (ADC)  22  receives a tested signal output from tested PLL  11  and converts the received signal into a digital signal. Analytic signal converting unit  23  converts digital tested signal x c (t) into analytic signal z c (t) represented by a complex function. In the present embodiment, tested signal x c (t) is the clock signal and is represented by the following formula.
 
 x   c ( t )= A   c  cos(2 πf   c   t+Θ   c −Δφ( t ))  (11)
 
A c  is amplitude of the clock signal, f c  is frequency of the tested signal, θ c  is an initial phase angle, and Δφ(t) is wobbling of a phase (phase noise waveform). In the present embodiment, analytic converting unit  23  is a Hilbert conversion-generator to perform Hilbert conversion for clock signal x c (t), and has a bandwidth filter (not shown) and Hilbert converting unit  25 .
 
   In analytic converting unit  23 , the bandwidth filter extracts a signal component around a fundamental frequency of received clock signal x c (t). Hilbert converting unit  25  performs Hilbert conversion for clock signal x c (t) by the following formula.
 
 {circumflex over (x)}   c ( t )= H[x   c ( t )]= A   c  sin(2 πf   c   t+Θ   c −Δφ( t ))  (12)
 
Analytic signal converting unit  23  outputs analytic signal z c (t) of which x c (t) and {circumflex over (x)} c (t) are respectively a real number and an imaginary number. 
                       z   c     ⁡     (   t   )       =       ⁢         x   c     ⁡     (   t   )       +         x   ^     c     ⁡     (   t   )                     =       ⁢         A   c     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f   c     ⁢   t     +     Θ   c     -     Δ   ⁢           ⁢     ϕ   ⁡     (   t   )           )         +       jA   c     ⁢     sin   ⁡     (       2   ⁢   π   ⁢           ⁢     f   c     ⁢   t     +     Θ   c     -     Δ   ⁢           ⁢     ϕ   ⁡     (   t   )           )                         (   13   )             
 
   Instantaneous phase estimating unit  26  estimates instantaneous phase θ(t) of clock signal x c (t) by the following formula.
 
Θ( t )=[2 πf   c   t+Θ   c −Δφ( t )]mod 2π c −Δφ( t )[rad]  (14)
 
   Linear phase remover  27  outputs phase noise wave form Δφ(t) by removing a linear phase from instantaneous phase θ(t). Linear phase remover  27  includes continuous image phase converting unit  28 , linear phase evaluator  29 , and subtracter  31 . 
   Continuous phase converting unit  28  converts instantaneous phase θ(t) into continuous phase θ(t) by an unwrapping method.
 
θ( t )=2 πf   c   t+Θ   c −Δφ( t )[rad]  (15)
 
   Linear phase evaluator  29  estimates a linear phase of continuous phase θ(t), that is, a linear instantaneous phase of an ideal signal without jitter. Linear phase evaluator  29  directly conforms by a line-trend estimating method, that is, a minimum square method for received continuous phase θ(t), and estimates linear instantaneous phase [2πf c t+θ c ]. 
   Subtracter  31  receives linear instantaneous phase [2πf c t+θ c ] and continuous phase θ(t). Subtracter  31  calculates a variance term of instantaneous phase θ(t), that is, phase noise waveform Δφ(t) by removing continuous phase θ(t) from linear instantaneous phase [2f c t+θ c ]. 
   Zero cross sampler  43  outputs timing jitter sequence Δφ[n], which is set of a randomly sampling value by sampling phase noise waveform Δφ(t). Peak-to-peak detecting unit  32  outputs peak-to-peak value Δφ pp  of timing jitter by calculating a difference of a maximum peak value of Δφ[n], max(Δφ[k]) and a minimum peak value of Δφ[n], min(Δφ[k]). 
               Δϕ     RM   ⁢           ⁢   S       =         1   N     ⁢       ∑     k   =   0       N   -   1       ⁢     Δ   ⁢           ⁢       ϕ   2     ⁡     [   n   ]                       (   17   )             
 
   Square mean detecting unit  33  receives timing jitter sequence Δφ[n]. Square mean detecting unit  33  calculates square mean (RMS) value Δφ RMS  of timing jitter by the following formula. 
               Δ   ⁢           ⁢     ϕ   pp       =         max   k     ⁢     (     Δ   ⁢           ⁢     ϕ   ⁡     [   k   ]         )       -       min   k     ⁢     (     Δ   ⁢           ⁢     ϕ   ⁡     [   k   ]         )                 (   16   )             
 
   As described above, the peak-to-peak value and square mean of timing jitter can be obtained from phase noise wave Δφ(t). A method to obtain the peak-to-peak value and square mean of timing jitter from phase noise wave Δφ(t) is defined as a Δφ method. 
   The jitter estimating apparatus of the present invention can measure period jitter. Analytic signal z(t) of basic cosine wave x(t) of the tested signal is given by the following formula. 
                     z   ⁡     (   t   )       =       ⁢       x   ⁡     (   t   )       +     jH   ⁡     [     x   ⁡     (   t   )       ]                     =       ⁢       A   ⁢           ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f   0     ⁢   t     +   θ   -     Δ   ⁢           ⁢     ϕ   ⁡     (   t   )           )         +     jA   ⁢           ⁢     sin   ⁡     (       2   ⁢   π   ⁢           ⁢     f   0     ⁢   t     +   θ   -     Δ   ⁢           ⁢     ϕ   ⁡     (   t   )           )                         (   18   )             
 
Where f 0  is a fundamental frequency of the tested signal and f 0  is 1/T 0 . (T 0  is a fundamental period). An instantaneous frequency (Hz) of analytic signal z(t) is given by the following formula. 
               1       T   0     +   J       =         ω   ⁡     (   t   )         2   ⁢   π       =       1     2   ⁢   π       =             x   ⁡     (   t   )       ⁢       H   ′     ⁡     [     x   ⁡     (   t   )       ]         -         x   ′     ⁡     (   t   )       ⁢     H   ⁡     [     x   ⁡     (   t   )       ]                 x   2     ⁡     (   t   )       +       H   2     ⁡     [     x   ⁡     (   t   )       ]           ⁢     
     ⁢           =       1     T   0       ⁢     (     1   -         T   0       2   ⁢   π       ⁢   Δ   ⁢           ⁢       ϕ   ′     ⁡     (   t   )           )                     (   19   )             
 
Therefore, the formula (20) is given as follows: 
                 T   0     +     J   ⁡     (   t   )         ≈       T   0     ⁡     (     1   -         T   0       2   ⁢   π       ⁢   Δ   ⁢           ⁢       ϕ   ′     ⁡     (   t   )           )               (   20   )             
 
Timing jitter sequence is obtained by sampling phase noise waveform Δφ(t) with timing (approximate zero cross point), which is close to each zero cross point of real number part x(t) in analytic signal z(t). In this case, it is preferable that the approximate zero cross point is timing, which is the closest to each zero cross point.
 
   Period jitter J is calculated as difference sequence of the timing jitter sequence by the following formula. In this case, period jitter J may be calculated as sampling interval T k,k+1  of the approximate zero cross point is substantially equal to period T 0  of the tested signal. 
               J   ⁡     [   k   ]       =         Δϕ   ⁡     [     k   +   1     ]       -     Δ   ⁢           ⁢     ϕ   ⁡     [   k   ]               2   ⁢   π       T   0                 (   21   )             
 
Unit radian is converted into a second by the denominator 2π/T 0 .
 
In case of T 0 ≠T k,k+1 , period jitter J may be calculated by the following formula. 
               J   ⁡     [   k   ]       =           Δϕ   ⁡     [     k   +   1     ]       -     Δ   ⁢           ⁢     ϕ   ⁡     [   k   ]               2   ⁢   π       T   0         ⁢     (       T   0       T     k   ,     k   +   1           )               (   22   )             
 
T 0 /T k,k+1  is a correction term for a formula (21).
 
     FIG. 12  illustrates RMS value J RMS  and peak-to-peak value J pp  of period jitter of the tested signal having sine wave jitter. In this figure, there are shown the period jitters, calculated by the Δφ method using the formula (21), and by a correction Δφ method using the formula (22), that is, the correction term. Period jitter can be calculated precisely by calculating period jitter using the Δφ method. Period jitter can be calculated further precisely by calculating period jitter using a correction Δφ method. 
   In a case of calculating period jitter, the period may be m period (m=0.5, 1, 2, 3, . . . ). Period jitter may be calculated based on a difference between timing jitter at a prescribed rise (or fall) zero cross point and a next fall (rise) zero cross point of the prescribed rise (fall) zero cross point of the tested signal where m=0.5. Period jitter may be calculated based on a difference between timing jitter at a prescribed rise (or fall) zero cross point and a second rise (fall) zero cross point from the prescribed rise (fall) zero cross point of the tested signal where m=2. RMS detecting unit  33  and peak-to-peak detecting unit  32  respectively calculates RMS value J RMS  and peak-to-peak value J pp  of period jitter by the following formulas (23) and (24). 
               J     RM   ⁢           ⁢   S       =         1   M     ⁢       ∑     k   =   1     M     ⁢       J   2     ⁡     [   k   ]                     (   23   )                 J   pp     =         max   k     ⁢     (     J   ⁡     [   k   ]       )       -       min   k     ⁢     (     J   ⁡     [   k   ]       )                 (   24   )             
 
(where M is the number of samplings of data constituting calculated period jitter.)
 
     FIG. 13A  illustrates histogram of period jitter measured by a time interval analyzer.  FIG. 13B  illustrates histogram of period jitter measured by the jitter estimating apparatus of the present invention. In these figures, abscissas shows time and ordinates shows the number of events (number of zero cross points). 
     FIG. 14  illustrates the number of events, RMS value of period jitter, and a peak-to-peak value of period jitter. In  FIG. 14 , a formula of J pp =45 ps is a correct value in approximate number of 5000 events. In  FIG. 14 , error is calculated by considering 45 ps as a true value. As seen from  FIGS. 13A ,  13 B, and  14 , the jitter estimating apparatus of the present invention can calculate jitter of the tested signal with high precision in a short time. 
   Further, the jitter estimating apparatus of the present invention can also measure cycle-to-cycle period jitter J cc . Cycle-to-cycle period jitter J cc  is period variance between continuous cycle periods and is represented by the following formula. 
                 J   cc     ⁡     [   k   ]       =         T   ⁡     [     k   +   1     ]       -     T   ⁡     [   k   ]         =         (       T   0     +     J   ⁡     [     k   +   1     ]         )     -     (       T   0     +     J   ⁡     [   k   ]         )       ⁢     
     ⁢           =       J   ⁡     [     k   +   1     ]       -     J   ⁡     [   k   ]                     (   25   )             
 
   A difference of obtained data of period jitter is calculated and square mean of the difference, and a difference between a maximum value and a minimum value are calculated. RMS detecting unit  33  calculates RMS value J cc,RMS  of cycle-to-cycle period jitter by the following formula (26). 
               J     CC   ,     RM   ⁢           ⁢   S         =         1   L     ⁢       ∑     k   =   1     L     ⁢       J   CC   2     ⁡     [   k   ]                     (   26   )             
 
Peak-to-peak detecting unit  32  calculates peak-to-peak value J cc,pp  of cycle-to-cycle period jitter by the following formula (27). 
               J     CC   ,   PP       =         max   k     ⁢     (       J   CC     ⁡     [   k   ]       )       -       min   k     ⁢     (       J   CC     ⁡     [   k   ]       )                 (   27   )             
 
(where L is the number of samplings of data constituting measured cycle-to-cycle period jitter.)
 
   The jitter estimating apparatus of the present invention may calculate timing jitter Δφ[n] by sampling phase noise waveform Δφ(t) in timing close to each zero cross point of real number part x(t) in analytic signal z(t) as aforementioned above, preferably, the timing which is the closest to each zero cross point. Moreover, the jitter estimating apparatus may calculate timing jitter Δφ[n] by further providing an interpolating unit to interpolate data constituting phase noise waveform at each zero cross point by an interpolating method or an inverse interpolating method. 
     FIG. 15  illustrates another example of the jitter estimating apparatus of the present invention. A configuration with the same reference numeral as in  FIG. 11  has the same or similar function as/to  FIG. 11 . 
   The jitter estimating apparatus has analytic signal converting unit  23 , instantaneous phase estimating unit  26 , linear phase remover  27 , jitter sequence estimating unit  62 , worst value estimating unit  41 , and probability estimating unit  54 . Jitter sequence estimating unit  62  includes zero cross sampler  43 , period jitter estimating unit  51 , and cycle-to-cycle period jitter estimating unit  52  which are one example of the timing jitter estimating unit. Worst value estimating unit  41  includes absolute value calculator  44 , maximum value detecting unit  45 , and a constant multiplying means comprising double unit  48  and quadruple unit  46 . Probability estimating unit  54  includes RMS detecting unit  55 , memory  56 , and probability calculator  57 . The jitter estimating apparatus in the present embodiment provides switch  42  to switch whether any of linear phase remover  27  and zero cross sampler  43  connects to worst value estimating unit  41 , and switch  53  to switch whether any of linear phase mover  27 , zero cross sampler  43 , period jitter estimating unit  51 , and cycle-to-cycle period jitter estimating unit  52  connects to probability estimating unit  54 . 
   Worst value estimating unit  41  receives phase noise waveform Δφ output from linear phase remover  27  or timing jitter sequence Δφ[n] output from zero cross sampler  43 . Absolute value calculator  44  calculates an absolute value of received phase noise waveform Δφ(t) or an absolute value of timing jitter sequence Δφ[n] in worst value estimating unit  41 . Since phase noise wave Δφ(t) and timing jitter sequence Δφ[n] are digital data, all of sign bits are converted into positive values in absolute value calculator  44 . 
   Maximum value detecting unit  45  detects an absolute maximum value (peak value) of phase noise waveform Δφ(t) or an absolute maximum value of timing jitter sequence Δφ[n]. That is, maximum value detecting unit  45  detects maximum value Δφmax of timing jitter described in  FIG. 1B . Quadruple unit  46  calculates worst value Ĵ pp  of period jitter in the tested signal by quadrupling maximum value Δφmax of timing jitter and the calculated value is output to output terminal  47 .
 
 Ĵ   pp =4Δφmax
 
   Double unit  48  may output worst value Ĵ pp  of period jitter in the tested signal by doubling maximum value Δφmax of timing jitter. The constant multiplying means may have a means to calculate a peak value of the tested signal and/or a worst value of the peak-to-peak value by multiplying a received maximum value by approximate integer. 
   A positive maximum peak and a negative maximum peak of period jitter have to be obtained before the maximum value of the peak-to-peak value, i.e., worst value Ĵ pp  of period jitter is calculated for the first time according to a conventional time interval analyzer method. Thereby, an extremely long time to calculate the worst value is required. However, since the jitter estimating apparatus in the present embodiment can estimate period jitter of the tested signal by providing worst estimating unit  41  when maximum value Δφmax of timing jitter of the tested signal is obtained, the jitter estimating apparatus can estimate worst value Ĵ pp  of period jitter in an extremely short time. 
   The jitter estimating apparatus of the present embodiment can estimate probability in which the peak-to-peak value of each jitter of the tested signal exceeds a prescribed value. In this case, zero cross sampler  43  outputs a prescribed sample value sequence and a sample value sequence one-delayed from the prescribed sample value of the tested signal. Period jitter estimating unit  51  receives the prescribed sample value sequence and the one-delayed sample value sequence, and then outputs the prescribed period jitter sequence and the one-delayed period jitter sequence. 
   Switch  53  switches whether any of linear phase mover  27 , zero cross sampler  43 , period jitter estimating unit  51 , and cycle-to-cycle period jitter estimating unit  52  connects to probability estimating unit  54 . 
   Memory  56  stores a set value to compare with the peak-to-peak value to calculate probability in which the peak-to-peak value of each jitter of the tested signal exceeds the prescribed value. In the present embodiment, memory  56  stores set values Δ{circumflex over (φ)} k , Δ{circumflex over (φ)} pk , Ĵ pk , and Ĵ cc,pp  to calculate probability in which each peak-to-peak value of phase noise waveform Δφ(t), timing jitter, period jitter and cycle-to-cycle period jitter of the tested signal exceeds a prescribed value. The set value stored in memory  56  may freely be set by a measurer according to jitter to be measured in the tested signal. An operation that the jitter estimating apparatus estimates probability in which the peak-to-peak value of each jitter of the tested signal exceeds the prescribed value will be described below. 
   An operation to calculate probability in which the peak-to-peak value of phase noise waveform Δφ(t) of the tested signal exceeds set value Δ{circumflex over (φ)} k  is described. When probability in which the peak-to-peak value of phase noise waveform Δφ(t) exceeds set value Δ{circumflex over (φ)} k  is calculated, switch  53  connects linear phase remover  27  to probability estimating unit  54 . RMS detecting unit  55  receives phase noise waveform Δφ(t) output by linear phase remover  27  in probability estimating unit  54 . RMS detecting unit  55  calculates RMS value Δφ RMS  of phase noise in the tested signal based on a formula (17). 
   Probability calculator  57  reads set value Δ{circumflex over (φ)} k  stored in memory  56 . Probability calculator  57  receives RMS value Δφ RMS  of phase noise of the tested signal. Probability calculator  57  calculates probability P r (Δφ pp &gt;Δ{circumflex over (φ)} k ) in which peak-to-peak value Δφ pp  of phase noise waveform Δφ(t) of the tested signal exceeds set value Δ{circumflex over (φ)} k  from RMS value Δφ RMS  and set value Δ{circumflex over (φ)} k  based on the formula (10). In this case, probability is calculated under a condition of which Δφ RMS  is substituted for σ J  and Δ{circumflex over (φ)} k  is substituted for Ĵ pp  in the formula (10). Probability calculator  57  outputs calculated probability P r (Δφ pp &gt;Δ{circumflex over (φ)} k ) to output terminal  59 . 
     FIGS. 16A to 16B  illustrate real number part x c (t) of analytic signal z c (t), phase noise waveform Δφ(t), and period jitter J p (t). An operation to calculate probability in which the peak-to-peak value of timing jitter in the tested signal exceeds set value Δ{circumflex over (φ)} pk  will be described referring to  FIGS. 15 and 16A  to  16 C. 
   Zero cross point detecting unit  58 , provided between analytic signal converting unit  23  and zero cross sampler  43 , detects a sample point (calculation point) which is close to a zero cross point of real number part x c (t) in analytic signal z c (t) output from analytic signal converting unit  23 . In this case, the zero cross detecting unit preferably detects the sample point which is the closest to the zero cross point of real number x c (t). 
     FIG. 16A  illustrates one example of the sample point which is the closest to the zero cross point of real number part x c (t) detected by zero cross point detecting unit  58 . The sample point which is the closest to a detected zero cross point is shown with a circular mark and the sample point is an approximate zero cross point, in  FIG. 16A . 
   One example of an operation that zero cross point detecting unit  58  detects the approximate zero cross point is described. Level V (50%) of 50% of the maximum value and the minimum value is calculated as a level of zero cross in a case where a maximum value of waveform of real number part x c (t) in the analytic signal is a level of 100% and a minimum value is a level of 0%. Differences, (x c (j- 1 )−V(50%)) and (x c (j)−V(50%)), of each adjacent sample value ((j- 1 )-th value, j-th value) in sampling values of real number part x c (t) and the level V of 50% are calculated, and these multiplied values are further calculated.
 
( x   c ( j - 1 )− V (50%))×( x   c ( j )− V (50%))
 
In a case where x c (t) crosses a level of 50%, that is, a zero level, between (j- 1 )-th value and j-th value, sign of a (j- 1 )-th sample value (x c (j- 1 )−V(50%)) or a j-th sample value (x c (j)−V(50%)) changes from a negative to a positive or from the positive to the negative. The sign of multiplied value is changed to the negative when x c (t) crosses the zero level. Zero cross point detecting unit  58  outputs either of j- 1 -th sample value (x c (j- 1 )−V(50%)) or j-th sample value (x c (j)−V(50%)), which has the smaller absolute value of the two, as the approximate zero cross point, in the case where x c (t) crosses a level of 50%, that is, a zero level, between (j- 1 )-th value and j-th value. Zero cross point detecting unit  58  outputs timing in which the calculated approximate zero cross point is sampled.
 
   Zero cross sampler  43  receives timing of the approximate zero cross point from zero cross point detecting unit  58 . Zero cross sampler  43  samples phase noise waveform Δφ(t) output by linear phase remover  27  based on timing of the received approximate zero cross point, that is, timing shown by the circular mark in  FIG. 16B . The sample value of phase noise waveform Δφ(t) sampled by zero cross sampler  43  shows shift amount out of ideal zero cross timing of real number part x c (t) in the analytic signal without jitter, that is, timing jitter. 
   In a case where probability in which the peak-to-peak value of timing jitter exceeds set value Δ{circumflex over (φ)} pk  is calculated, switch  53  connects zero cross sampler  43  to probability estimating unit  54 . Probability estimating unit  54  receives a sample value output from zero cross sampler  43 . 
   RMS detecting unit  55  receives a sample value sequence, which is set of randomly sample value output from zero cross sampler  43 , that is, timing jitter sequence in probability estimating unit  54 . RMS detecting unit  55  calculates RMS value Δφ RMS  of timing jitter of a tested signal from timing jitter sequence based on the formula (17). 
   Probability calculator  57  reads set value Δ{circumflex over (φ)} pk  stored in memory  56 . Probability calculator  57  receives RMS value Δφ RMS  of timing jitter of the tested signal. Probability calculator  57  calculates probability P r (Δφ pp &gt;Δ{circumflex over (φ)} pk ) in which peak-to-peak value Δφ pp  of timing jitter Δφ[k] of the tested signal exceeds set value Δ{circumflex over (φ)} pk  from RMS value Δφ RMS  and set value Δ{circumflex over (φ)} pk  based on the formula (10). In this case, probability is calculated under a condition of which Δφ RMS  is substituted for σ and Δ{circumflex over (φ)} pk  is substituted for Ĵ pp  in the formula (10). Probability calculator  57  outputs calculated probability P r (Δφ pp &gt;Δ{circumflex over (φ)} pk ) to output terminal  59 . 
   An operation to calculate probability in which the peak-to-peak value of period jitter J of the tested signal exceeds the set value Ĵ pk  will be described referring to  FIG. 15  and  FIGS. 16A to 16C . 
   Period jitter estimating unit  51  receives two sequences. Period jitter estimating unit  51  calculates wobbling between zero cross points, that is, period jitter J p  by calculating a difference between timing jitter in prescribed timing and timing jitter in next timing of prescribed timing with respect to each timing jitter Δφ[k]. For example, period jitter estimating unit  51  calculates a difference Δφ n+1 −Δφ n  between n-th sample value Δφ n  and (n+1)-th sample value Δφ n+1  of Δφ(t) as period jitter J p  as shown in  FIG. 16B . By this way, period jitter estimating unit  51  calculates sequence of period jitter J p  as shown in  FIG. 16C  by sequentially calculating period jitter J p  and outputs the calculated value. 
   In a case where probability in which the peak-to-peak value of period jitter exceeds set value Ĵ pk  is calculated, switch  53  connects period jitter estimating unit  51  to probability estimating unit  54 . Probability estimating unit  54  receives period jitter J p  or period jitter sequence J[k] output from period jitter estimating unit  51 . RMS detecting unit  55  calculates RMS value J RMS  of period jitter of the tested signal from period jitter sequence based on the following formula or the formula (23). 
               J     RM   ⁢           ⁢   S       =       σ   J     =         1   N     ⁢       ∑     n   =   0       N   -   1       ⁢       J   p   2     ⁡     (   n   )                       (   28   )             
 
   Probability calculator  57  reads set value Ĵ pk  stored in memory  56 . Probability calculator  57  receives RMS value J RMS  of period jitter of the tested signal. Probability calculator  57  calculates probability P r (J pp &gt;Ĵ pk ) in which peak-to-peak value J pp  of period jitter J[k] of the tested signal exceeds setting value Ĵ pk  from RMS value J RMS  and set value Ĵ pk  based on the formula (10). In this case, probability is calculated under a condition of which J RMS  is substituted for σ J  and Ĵ pk  is substituted for Ĵ pp  in the formula (10). Probability calculator  57  outputs calculated probability P r (J pp &gt;Ĵ pk ) to output terminal  59 . 
   In another embodiment, probability estimating unit  54  may receive output of worst value estimating unit  41  and estimate probability. In this case, probability calculator  57  receives RMS value σ J  of period jitter and Ĵ pk =2Δφmax calculated in double unit  48 . Probability calculator  57  calculates probability P r (J p &gt;Ĵ pk ) in which peak value J p  of period jitter of the tested signal exceeds set value Ĵ pk  by the formula (2), that is, the following formula. 
           P   r     ⁡     (       J   p     &gt;       J   ^     pk       )       =     exp   ⁡     (     -         J   ^     pk   2       2   ⁢     σ   J   2           )           
 
Probability calculator  57  outputs probability P r (J p &gt;Ĵ pk ) in which peak value J p  of period jitter of the tested signal exceeds set value Ĵ pk  to output terminal  59 . Probability calculator  57  may receive RMS value σ J  of period jitter and Ĵ pk =4Δφmax calculated in quadruple unit  46 , calculate probability P r (J pp &gt;Ĵ pk ) in which peak-to-peak value J pp  of period jitter of the tested signal exceeds set value Ĵ pk  based on the formula (10), and output the calculated value to output terminal  59 .
 
     FIG. 17  illustrates a configuration of period jitter estimating unit  51 . Period jitter estimating unit  51  includes interval calculator  51   a , calculator  51   b , correction unit  51   c , and delay unit  51   d . Interval calculator  51   a  receives a zero cross sample pulse from zero cross point detecting unit  58 . Interval calculator  51   a  calculates an interval between edges of each zero cross sample pulses which are adjacent to each other, for example, interval T k·k+1  between k-th edge and (k+1)-th edge. 
   Calculator  51   b  receives timing jitters of edges which are adjacent to each other in the tested signal, for example, k-th timing jitter Δφ[k] and (k+1)-th timing jitter Δφ[k+1] from zero cross sampler  43 . Calculator  5   b  calculates period jitter sequence J[k] by the formula (21). Calculator  51   b  converts a unit of period jitter sequence J[k]by multiplying calculated period jitter sequence J[k] by T 0 /2π. 
   Correcting unit  51   c  receives interval T k·k+1  calculated in interval calculator  51   a  and period jitter sequence J[k] calculated in calculator  51   b . Correcting unit  51   c  calculates period jitter sequence J[k] corrected by multiplying period jitter sequence by correct term T 0 /T k·k+1  based on the formula (22). Period jitter sequence J[k] calculated in correcting unit  51   c  is output from period jitter estimating unit  51  and is supplied to delay unit  51   d . Delay unit  51   d  delays received period jitter sequence J[k] for one period to output delayed period jitter sequence J[k]. 
   Probability in which peak-to-peak value J pp  of period jitter exceeds set value Ĵ pk  can be calculated precisely by providing correcting unit  51   c  to calculate period jitter sequence J[k] by the formula (22), that is, by using correct term. 
   An operation to calculate probability in which peak-to-peak value J cc,pk  of cycle-to-cycle period jitter J cc  of the tested signal exceeds set value Ĵ cc,pk  will be described. Cycle-to-cycle period jitter estimating unit  52  sequentially receives adjacent period jitter J[k] and J[k+1] calculated in period jitter estimating unit  51 . Cycle-to-cycle period jitter estimating unit  52  calculates different value J cc [k] between adjacent jitters by the formula (25).
 
 J   cc   [k]=J[k+ 1 ]−J[k] 
 
Cycle-to-cycle period jitter estimating unit  52  outputs cycle-to-cycle sequence J cc [k].
 
   In a case where probability in which peak-to-peak value J cc,pk  of cycle-to-cycle period jitter J cc  exceeds set value Ĵ cc,pk  is calculated, switch  53  connects cycle-to-cycle period jitter estimating unit  52  to probability estimating unit  54 . Probability estimating unit  54  receives cycle-to-cycle jitter sequence J cc [k] output from cycle-to-cycle period jitter estimating unit  52 . 
   RMS detecting unit  55  calculates RMS value J cc,RMS  of cycle-to-cycle period jitter of the tested signal from cycle-to-cycle jitter sequence J cc [k] based on the formula (26). 
   Probability calculator  57  reads set value Ĵ cc,pk  stored in memory  56 . Probability calculator  57  receives RMS value J cc,RMS  of period jitter of the tested signal. Probability calculator  57  calculates probability P r (J cc,pp &gt;Ĵ cc,pk ) in which peak-to-peak value J cc,pp  of cycle-to-cycle period jitter J cc [k] of the tested signal exceeds Ĵ cc,pk  from RMS value J cc,RMS  and set value Ĵ cc,pk  based on the formula (10). In this case, probability is calculated under a condition of which J cc,RMS  is substituted for σ J  and Ĵ cc,pk  is substituted for Ĵ pp  in the formula (10). Probability calculator  57  outputs calculated probability P r (J cc,pp &gt;Ĵ cc,pk ) to output terminal  59 . 
   In the jitter estimating apparatus of this embodiment, memory  56  may store various set values to calculate probability in which the peak value of jitter exceeds the prescribed value. In this case, probability calculator  57  reads a desired set value from memory  56  according to various jitters to be measured and calculates probability in which the peak value of jitter exceeds the set value based on the formula (2). 
   In a case where probability in which the peak-to-peak value of various jitter exceeds the set value is calculated, probability estimating unit  54  may further have a constant multiplying means to multiply RMS value of various jitter, which is calculated by RMS detecting unit  55 , by 2K (K is positive constant). In this case, probability calculator  57  receives a value calculated by the constant multiplying means as set value Ĵ pk  and calculates probability in which the peak-to-peak value of various jitter exceeds the set value by the formula (10). 
   In a case where probability in which the peak value of various jitter exceeds the set value is calculated, probability estimating unit  54  may further have a constant multiplying means to multiply RMS value of various jitter, which is calculated by RMS detecting unit  55 , by K (K is positive constant). In this case, probability calculator  57  receives the value calculated by the constant multiplying means as set value Ĵ pk  and calculates probability in which the peak-to-peak value of various jitter exceeds the set value based on the formula (10). 
   The jitter estimating apparatus may further provide waveform clipper  67 . Waveform clipper  67  receives the tested signal output from tested PLL  11 , shapes signal waveform of the tested signal, and supplies the shaped tested signal to ADC  22 . The jitter estimating apparatus can keep amplitude of the tested signal substantially constant by providing waveform clipper  67 . Influence on phase noise waveform Δφ(t) can be reduced greatly by amplitude modulation. Jitter can be measured more precisely. In another example, ADC  22  may perform a process similar to a process of waveform clipper  67 . 
   The jitter estimating apparatus may further provide low frequency component remover  98  for receiving phase noise waveform Δφ(t) to remove the low frequency component from phase noise waveform Δφ(t). In this case, switch  42  preferably connects either low frequency component remover  98  or zero cross sampler  43  to worst value estimating unit  41 . Switch  53  preferably connects either low frequency component remover  98 , zero cross sampler  43 , period jitter estimating unit  51  or the cycle-to-cycle period jitter estimating unit to probability estimating unit  54 . The jitter estimating apparatus can remove low frequency component sufficiently lower than frequency of tested signal x c (t) by providing low frequency component remover  98 . It is possible to prevent overestimating peak-to-peak jitter. 
     FIGS. 18A and 18B  illustrate relationship between peak-to-peak value of timing jitter Δφ in the clock signal (tested signal) and the number of event, the clock signal being output by the microprocessor and estimated by the jitter estimating apparatus of the present invention.  FIG. 18A  illustrates a case of a quiescent mode and  FIG. 18B  illustrates a case of a noisy mode. An ordinate axis shows peak-to-peak value Δφ pp  and an abscissas axis shows the number of events. 
   Solid line shows theoretical curve of timing jitter and a circular mark shows timing jitter estimated by the jitter estimating apparatus of the present invention in  FIGS. 18A and 18B .  FIGS. 18A and 18B  describe that the jitter estimating apparatus of the present invention can precisely estimate jitter. Practically, since jitter in the noisy mode specially becomes a problem in a case where a microprocessor is used, it is preferable that jitter can be estimated precisely in the noisy mode. The jitter estimating apparatus in the present invention can estimate generation probability of timing jitter extreme precisely even when the microprocessor operates in the noisy mode. 
     FIGS. 19A and 19B  illustrate relationship between peak-to-peak value of period jitter J p  in the clock signal (tested signal) and the number of event, the clock signal being output by the microprocessor and estimated by the jitter estimating apparatus of the present invention.  FIG. 19A  illustrates the case of quiescent mode and  FIG. 19B  illustrates the case of noisy mode. The ordinate axis shows peak-to-peak value J pp  and the abscissa axis shows the number of events. 
   Solid line shows theoretical curve of period jitter and the circular mark shows period jitter estimated by the jitter estimating apparatus of the present invention in  FIGS. 19A and 19B .  FIGS. 19A and 19B  describe that the jitter estimating apparatus of the present invention can precisely estimate generation probability of period jitter. 
     FIGS. 20A and 20B  illustrate relationship between peak-to-peak value of cycle-to-cycle period jitter J p  in the clock signal (tested signal) and the number of event, the clock signal being output by the microprocessor and estimated by the jitter estimating apparatus of the present invention.  FIG. 20A  illustrates the case of quiescent mode and  FIG. 20B  illustrates the case of noisy mode. The ordinate axis shows peak-to-peak value J pp  and the abscissa axis shows the number of events. 
   Solid line shows the theoretical curve of period jitter and the circular mark shows period jitter estimated by the jitter estimating apparatus of the present invention in  FIGS. 20A and 20B .  FIGS. 20A and 20B  describe that the jitter estimating apparatus of the present invention can precisely estimate generation probability of cycle-to-cycle period jitter. 
     FIG. 21  illustrates zero cross points number to estimate period jitter. Curves  65   a  and  65   b  show a theoretical value calculated from reciprocal of probability calculated by the formula (2). A lower abscissa axis shows the zero cross point number of curve  65   a  and an upper abscissa axis shows the zero cross point number of curve  65   b . A Δ mark shows the peak value of period jitter in the quiescent mode calculated by a Δφ method and a ▾ mark shows the peak value of period jitter in the quiescent mode calculated by the time interval analyzer. The ◯ mark shows the peak value of period jitter in the noisy mode calculated by the Δφ method and a ▪ mark shows the peak value of period jitter in the noisy mode calculated by the time interval analyzer. The Δφ method makes 4Δφmax to be the worst value J′ pp  and broken line  66  shows the value of J′ pp /2σ J . 
   The peak value of period jitter calculated by the Δφ method is almost consistent with the theoretical value and it can be seen that the peak value of period jitter is accordance with Rayleigh distribution. According to the time interval analyzer, the worst value of period jitter is obtained at a point of zero cross point number of 10 5  in only noisy mode. However, according to the Δφ method in the present invention, it can be seen that a measured value is consistent with curve  65   a , which is the theoretical value, around the point of zero cross point number of 10 3 . The worst value of period jitter in the case is shown by broken line  66 . 
   According to a conventional time interval analyzer method, a zero cross point number of 10 5  is needed to calculate the worst value of period jitter even in the noisy mode, however, only a zero cross point number of 10 3  is needed by the Δφ method in the present invention. Jitter of the tested signal can be estimated in an extreme short time. 
     FIG. 22  illustrates measured values of jitter measured by the time interval analyzer and the Δφ method.  FIG. 22  illustrates peak-to-peak value J pp  by the time interval analyzer method, as well as timing jitter peak value Δφ p , worst value J pp  of the period jitter, and probability P r (J p ) by a Δφ method of the present invention, in the quiescent mode and in the noisy mode and the number of zero cross points used for measurement. Regarding the value of the Δφ method, the values of the two cases are shown, e.g., a case where amplitude modulation does not occur in the tested signal in which phase modulation by jitter occurs (PM) and a case where amplitude modulation occurs (PM+AM) 
   A maximum value (worst value) of peak-to-peak of period jitter can be calculated by 997 zero cross points according to the Δφ method, in contrast, it can be seen that 102000 zero cross points is needed by the conventional time interval analyzer method. In the time interval analyzer method, values of J pp  are greatly different between a case where a number of zero cross points is 500 and a case where a number of zero cross points is 102000, and values of J pp  cannot be measured in the case where a number of zero cross points is 500, correctly. The jitter estimating apparatus by the Δφ method in the present invention can estimate jitter further precisely in the extreme short time. 
     FIG. 23  illustrates another embodiment of the jitter estimating apparatus in the present invention. A configuration having the same reference numerals as in  FIG. 15  has the same or similar function as/to configuration in  FIG. 15 . 
   Probability estimating unit  54  includes RMS detecting unit  55 , peak-to-peak detecting unit  61 , and probability calculator  57  in the present embodiment. Switch  53  connects either linear phase remover  27 , zero cross sampler  43 , period jitter estimating unit  51 , or cycle-to-cycle period jitter estimating unit  52  to RMS detecting unit  55  and peak-to-peak detecting unit  61  included in probability estimating unit  54 . 
   In a case where probability in which peak-to-peak value Δφ pp  in phase noise waveform Δφ(t) is generated is calculated, switch  53  connects linear phase remover  27  to probability estimating unit  54 . RMS detecting unit  55  and peak-to-peak detecting unit  61  receive phase noise waveform Δφ(t) output from linear phase remover  27 . 
   RMS detecting unit  55  calculates RMS value Δφ RMS  of phase noise waveform Δφ based on phase noise waveform Δφ(t). Peak-to-peak detecting unit  61  calculates peak-to-peak value Δφ pp  of phase noise waveform Δφ(t). Probability calculator  57  receives RMS value Δφ RMS  and peak-to-peak value Δφ pp  of phase noise waveform Δφ(t). 
   Probability calculator  57  calculates probability in which peak-to-peak value Δφ pp  of phase noise waveform Δφ(t) is generated based on RMS value Δφ RMS  and peak-to-peak value Δφ pp  of phase noise waveform Δφ(t). 
   In a case where probability in which peak-to-peak value Δφ pp  of timing jitter Δφ[k] is generated is calculated, switch  53  connects zero cross sampler  43  to probability estimating unit  54 . RMS detecting unit  55  and peak-to-peak detecting unit  61  receive timing jitter Δφ[k] output from zero cross sampler  43 . 
   RMS detecting unit  55  calculates RMS value Δφ RMS  of timing jitter Δφ[k] by the formula (17) based on timing jitter Δφ[k]. Peak-to-peak detecting unit  61  calculates peak-to-peak value Δφ pp  of timing jitter Δφ[k] by the formula (16). 
   Probability calculator  57  receives RMS value Δφ RMS  and peak-to-peak value Δφ pp  of timing jitter Δφ sequence [k]. Probability calculator  57  calculates probability in which peak-to-peak value Δφpp of timing jitter Δφ[k] is generated based on RMS value Δφ RMS  and peak-to-peak value Δφ pp  of timing jitter sequence Δφ[k]. 
   In a case where probability in which peak-to-peak value J pp  of period jitter J p  is generated is calculated, switch  53  connects period jitter estimating unit  51  to probability estimating unit  54 . RMS detecting unit  55  and peak-to-peak detecting unit  61  receive period jitter sequence J[k] output from period jitter estimating unit  51 . 
   RMS detecting unit  55  calculates RMS value J RMS  of period jitter J[k] by the formula (23) based on period jitter J[k]. Peak-to-peak detecting unit  61  calculates peak-to-peak value J pp  of period jitter J[k] by the formula (24). 
   Probability calculator  57  receives RMS value J RMS  and peak-to-peak value ΔJ pp  of period jitter J[k]. Probability calculator  57  calculates probability in which period jitter J[k] exceeds peak-to-peak value J pp  based on RMS value J RMS  and peak-to-peak value J pp  of period jitter J[k]. Probability calculator  57  receives RMS value J RMS  of period jitter J[k] and peak-to-peak value J pp . 
   In a case where probability in which peak-to-peak value J cc,pp  of cycle-to-cycle period jitter J cc  is generated is calculated, switch  53  connects cycle-to-cycle period jitter estimating unit  52  to probability estimating unit  54 . RMS detecting unit  55  and peak-to-peak detecting unit  61  receive cycle-to-cycle period jitter J cc  output from cycle-to-cycle period estimating unit  52 . 
   RMS detecting unit  55  calculates RMS value J cc,RMS  of cycle-to-cycle period jitter J cc  by the formula (26) based on cycle-to-cycle period jitter J cc . Peak-to-peak detecting unit  61  calculates peak-to-peak value J cc,pp  of cycle-to-cycle period jitter J cc  by the formula (27). 
   Probability calculator  57  receives RMS value J cc,RMS  and peak-to-peak value J cc,pp  of cycle-to-cycle period jitter J cc . Probability calculator  57  calculates probability in which peak-to-peak value J cc,pp  of cycle-to-cycle period jitter J cc  is generated is calculated based on RMS value J cc,RMS  and peak-to-peak value J cc,pp  of cycle-to-cycle period jitter J cc . 
   The jitter estimating apparatus in the present embodiment can also calculate probability in which a peak value in each of various jitter is generated. In this case, probability estimating unit  54  includes a peak detecting unit to calculate the peak value of jitter sequence. Probability calculator  57  receives the peak value calculated by the peak detecting unit and probability in which the peak value of jitter is generated can be calculated by the formula (2). 
   Jitter sequence estimating unit  62  may have a configuration of only zero cross sampler  43  or two configurations of zero cross sampler  43  and period jitter estimating unit  51  among zero cross sampler  43 , period jitter estimating unit  51 , and cycle-to-cycle period jitter estimating unit  52  in an example of the jitter estimating apparatus shown in  FIGS. 15 and 23 . In this case, switch  53  connects any included in jitter sequence estimating unit  62  to probability estimating unit  54 . 
   The jitter estimating unit may provide switch  53  so that two or three among linear phase remover  27 , zero cross sampler  43 , period jitter estimating unit  51 , and cycle-to-cycle period jitter estimating unit  52  are connected to probability estimating unit  54 . The jitter estimating apparatus may provide probability estimating unit  54  for each output of linear phase remover  27 , zero cross sampler  43 , period jitter estimating unit  51 , and cycle-to-cycle period jitter estimating unit  52 . RMS detecting unit  55  may supply a value prior to extraction of the square calculation in RMS detecting unit  55 , for example, a value shown by the following formula to probability calculator  57 . 
         σ   2     =       (     1   /   M     )     ⁢       ∑     k   =   1     M     ⁢           ⁢       J   2     ⁡     [   k   ]               
 
   The jitter estimating apparatus may further provide waveform clipper  67 . Waveform clipper  67  receives the tested signal output from tested PLL  11 , shapes signal waveform of the tested signal, and supplies the shaped tested signal to ADC  22 . The jitter estimating apparatus can keep substantially constant amplitude of the tested signal by providing waveform clipper  67 . Influence received by phase noise waveform Δφ(t) can be reduced greatly by amplitude modulation, and jitter can be measured precisely. In another example, ADC  22  may perform a process similar to a process of waveform clipper  67 . 
   The jitter estimating apparatus may further provide low frequency component remover  98  to receive phase noise waveform Δφ(t) and to remove low frequency component from phase noise waveform Δφ(t). In this case, switch  53  preferably connects any of low frequency component remover  98 , zero cross sampler  43 , period jitter estimating unit  51 , and the cycle-to-cycle period jitter estimating unit to the probability estimating unit  54 . The jitter estimating apparatus can remove low frequency sufficiently lower than frequency of tested signal x c (t) by providing low frequency component remover  98 . It is possible to prevent overestimating peak-to-peak jitter. 
     FIG. 24  illustrates one example of the analytic signal converting unit  23 . Analytic signal converting unit  23  includes frequency domain converting unit  71 , band pass filter (BPF)  72 , and time domain converting unit  73 . Frequency domain converting unit  71  receives the tested signal converted in ADC  22  and transforms the received tested signal into a two-sided spectrum signal in a frequency domain by high-speed Fourier transformation (FFT) for example. 
   In the present embodiment, band pass filter  72  shields a prescribed frequency component in the two-sided spectrum signal. Band pass filter  72  shields a negative frequency component in the two-sided spectrum signal and extracts a frequency component near a positive fundamental frequency in the tested signal. Band pass filter  72  may increase a level of the tested signal including the extracted frequency component. Time domain converting unit  73  transforms the tested signal supplied from band pass filter  72  into analytic signal z c (t) by inverse Fourier transformation (IFFT). 
   The jitter estimating apparatus may further have a frequency divider  85  to divide a frequency of the tested signal output from tested PLL  11 . The frequency of the tested signal can lower by providing frequency divider  85 . The jitter estimating apparatus may provide a frequency converting unit (not shown) to generate a signal with a difference frequency of a local signal without jitter substantially and the tested signal, and to supply the generated signal to analytic signal converting unit  23 . 
   The jitter estimating apparatus may have comparator  84  instead of ADC  22 . In this case, comparator  84  receives the tested signal, converts the tested signal into a logic high or a logic low based on reference voltage V R  supplied to comparator  84 . That is, comparator  84  converts the received signal into one-bit digital data to supply the converted data to analytic signal converting unit  23 . 
     FIG. 25  illustrates another example of analytic signal converting unit  23 . Analytic signal converting unit  23  has frequency mixing unit  81 , low pass filter  82 , and A/D converting unit  83 . Frequency mixing unit  81  mixes tested signal x c (t) with a signal with a prescribed frequency component. In the present embodiment, frequency mixing units  81   a  and  81   b  respectively perform frequency-mixing for tested signals x c (t) with cos(2π(f c +Δf)t+θ) and sin(2π(f c +Δf)t+θ). 
   Low pass filters  82   a  and  82   b  respectively calculate analytic signals obtained in the following formula by extracting a difference frequency component between signals each of which is frequency-mixed by frequency mixing units  81   a  and  81   b. 
 
 z   c ( t )=( A   c /2)[cos(2 πΔft +(θ−θ c )−Δφ( t ))+ j  sin(2 πΔft +(θ−θ c )−Δφ( t ))]
 
   Each of an A/D converting units  83   a  and  83   b  performs A/D conversion respectively for real number part and imaginary number part of the analytic signal z c (t), and supplies them to instantaneous phase estimating unit  26 . Analytic signal converting unit  23  may have comparator  84  instead of A/D converting unit  83  in another example. Comparator  84  converts each of a real number part and an imaginary number part of received analytic signal z c (t) into logic high or logic low, that is, one-bit digital data, and supplies the converted data to instantaneous phase estimating unit  26 . 
   The jitter estimating apparatus may further have frequency divider  85  to divide a frequency of the tested signal output from tested PLL  11 . The frequency of the tested signal can be lowered by having frequency divider  85 . The jitter estimating apparatus may provide a frequency converting unit (not shown) to generate a signal with a difference frequency between a local signal without jitter substantially and the tested signal, and to supply the generated signal to analytic signal converting unit  23 . 
     FIG. 26  illustrates another embodiment of analytic signal converting unit  23 . Analytic signal converting unit  23  includes buffer memory  91 , signal extraction unit  92 , windowing function multiplication unit  93 , frequency domain converting unit  94 , bandwidth limit unit  95 , time domain converting unit  96 , and amplitude correcting unit  97 . 
   Buffer memory  91  receives and stores a tested signal digitalized by A/D converting unit  22  (see  FIGS. 15 and 23 ). Signal extraction unit  92  extract tested signal stored in buffer memory  91 . Signal extraction unit  92  desirably extracts the signal by reduplicating data and one portion of the tested signal extracted previously, in a case where the tested signal stored in buffer memory  91  is extracted. 
   Windowing function multiplication unit  93  multiplies the signal extracted by signal extraction unit  92  by a windowing function. Frequency domain converting unit  94  converts the signal in which the windowing function is multiplied into two-sided spectrum signal in a frequency domain by high-speed Fourier transformation. Bandwidth limit unit  95  limits bandwidth of the two-sided spectrum signal. Bandwidth limit unit  95  extracts a frequency component around a fundamental frequency of the tested signal to a one-sided spectrum signal of which a negative frequency component is almost zero in the present embodiment. 
   Time domain converting unit  96  transforms a signal output from bandwidth limit unit  95  into a time domain signal by inverse high-speed-Fourier transformation. Amplitude correcting unit  97  calculates an analytic signal by multiplying the time domain signal by the inverse windowing function to output the multiplied signal. 
     FIG. 27  is a flowchart showing one example of the jitter estimating method in the present invention. The jitter estimating method will be described referring to  FIG. 15 . At first, the desired peak-to-peak value, for example, such as Ĵ pk  is stored in memory  56  (S 201 ). Next, the tested signal is converted into an analytic signal of which the bandwidth is limited by analytic signal converting unit  23  (S 202 ). An instantaneous phase of the tested signal is estimated by instantaneous phase estimating unit  26  using the analytic signal (S 203 ). 
   The linear phase component is removed from the obtained instantaneous phase by linear phase remover  27  and phase noise waveform Δφ(t) of the tested signal is estimated (S 204 ). Linear phase remover  27  and probability estimating unit  54  are connected by switching switch  53  and RMS value of phase noise waveform Δφ(t) is calculated by RMS detecting unit  55  (S 205 ). Probability, in which the peak-to-peak value of phase noise waveform Δφ(t) exceeds the set value is calculated by probability calculator  57  based on calculated RMS value and the set value set in S 201  (S 206 ). 
   Successively, timing jitter sequence is calculated by sampling phase noise waveform Δφ(t) with zero cross sampler  43  (S 207 ). In this case, it is preferable to sample data which is close to zero cross timing of phase noise waveform Δφ(t). Zero cross sampler  43  and probability estimating unit  54  are connected by switching switch  53 , and RMS value of timing jitter sequence is calculated by RMS detecting unit  55  (S 208 ). Probability in which the peak-to-peak value of timing jitter exceeds the set value is calculated by probability calculator  57  based on calculated RMS value and the set value (peak-to-peak value) set in S 201  (S 206 ). 
   Successively, period jitter sequence is calculated by period jitter estimating unit  51  based on the difference of timing jitter sequence (S 210 ). Next, period jitter estimating unit  51  and probability estimating unit  54  are connected by switching switch  53 , and RMS value of period jitter sequence is calculated by RMS detecting unit  55  (S 211 ). Probability in which the peak-to-peak value of period jitter exceeds the set value is calculated by probability calculator  57  based on calculated RMS value and the set value (peak-to-peak value) set in S 201  (S 212 ). 
   Further, cycle-to-cycle period jitter sequence is calculated by cycle-to-cycle period jitter estimating unit  52  based on the difference between period jitter sequences (S 213 ). Next, cycle-to-cycle period jitter estimating unit  52  and probability estimating unit  54  are connected by switching switch  53  and RMS value of cycle-to-cycle period jitter sequence is calculated by RMS detecting unit  55  (S 214 ). Probability in which the peak-to-peak value of cycle-to-cycle period jitter exceeds the set value is calculated by probability calculator  57  based on calculated RMS value and the set value (peak-to-peak value) set in S 201  (S 215 ). 
   The jitter estimating method of the present invention can also calculate probability in which the peak value of each kind of jitter exceeds the set value. In this case, a peak value to calculate probability in which the peak value of each kind of jitter exceeds the prescribed value is stored in memory  56  in S 201 . Probability in which the peak value of each jitter exceeds the set value is calculated by probability calculator  57  based on RMS value of each kind of jitter and the peak value stored in memory  56  in each of S 206 , S 209 , S 212 , and S 215 . 
     FIG. 28  illustrates a flowchart of another example of the jitter estimating method. The jitter estimating method will be described referring to  FIG. 23 . The same reference numeral as  FIG. 27  is applied for a step corresponding to  FIG. 27 . A step different from an example of the jitter estimating method described in  FIG. 27  will be described. 
   Since the peak-to-peak value is calculated in the jitter estimating method of the present embodiment, the method need not have a step (S 201 ) of storing the set value in memory  56  (see  FIG. 15 ). After RMS value of phase noise waveform is calculated in S 205 , the peak-to-peak value is calculated by peak-to-peak detecting unit  61  based on the difference between a maximum value and a minimum value of phase noise waveform (S 301 ). In S 206 , probability in which the peak-to-peak value of phase noise waveform is generated is calculated by probability calculator  57  based on RMS value and the peak-to-peak value calculated in S 301 . 
   After RMS value of timing jitter sequence is calculated in S 208 , the peak-to-peak value is calculated by peak-to-peak detecting unit  61  based on the difference of the maximum and the minimum value of timing jitter (S 302 ). In S 209 , probability in which the peak-to-peak value of timing jitter is generated is calculated by probability calculator  57  based on RMS value and the peak-to-peak value calculated in S 302 . 
   After RMS value of period jitter sequence is calculated in S 211 , the peak-to-peak value is calculated by peak-to-peak detecting unit  61  based on the difference of the maximum value and the minimum value of period jitter (S 303 ). In S 209 , probability in which the peak-to-peak value of period jitter is generated is calculated by probability calculator  57  based on RMS value and the peak-to-peak value calculated in S 303 . 
   After RMS value of cycle-to-cycle period jitter sequence is calculated in S 214 , the peak-to-peak value is calculated by peak-to-peak detecting unit  61  based on the difference of the maximum and the minimum value of cycle-to-cycle period jitter (S 304 ). In S 215 , probability in which the peak-to-peak value of cycle-to-cycle period jitter is generated is calculated by probability calculator  57  based on RMS value and the peak-to-peak value calculated in S 304 . 
   The jitter estimating method of the present invention can calculate probability in which the peak value of each jitter exceeds the set value. In this case, a peak value of each jitter is calculated by peak detecting unit, which can calculate the peak value of each jitter in S 301  to S 304 . Probability in which each jitter exceeds the peak value is calculated by probability calculator  57  based on each RMS value of jitter and the calculated peak value in each of S 206 , S 209 , S 212 , and S 215 . 
     FIG. 29  illustrates another example of linear phase remover  27 . Linear phase remover  27  in this example has zero cross sampler  43  between instantaneous phase estimating unit  26  and continuous phase converter  28  or between continuous phase converter  28  and linear phase evaluator  29 . Timing jitter sequence Δφ[n] may be calculated by sampling a signal output from instantaneous phase estimating unit  26  or continuous phase converter  28  at an approximate zero cross point. 
     FIG. 30  illustrates one part of a flowchart of a jitter estimating method for estimating jitter using linear phase remover  27  in  FIG. 29 . After an instantaneous phase of the tested signal is estimated in S 203 , the instantaneous phase is converted into a continuous instantaneous phase by continuous phase converting unit  28  (S 204   a ). An instantaneous linear phase is calculated by linear phase estimating unit  29  from the continuous instantaneous phase (S 204   b ). Noise phase waveform Δφ(t) is calculated by subtracter  31  by removing the instantaneous linear phase from the continuous instantaneous phase. 
   As shown in  FIG. 29 , in a case where zero cross sampler  43  is provided between instantaneous phase estimating unit  26  and continuous phase converting unit  28 , sample sequence of the instantaneous phase is calculated by approximate zero sampling of the instantaneous phase estimated in S 203  (S 401 ). In S 204   a , the continuous instantaneous phase is calculated based on the sample sequence. The continuous instantaneous linear phase is calculated in S 204  and timing jitter sequence Δφ[n] is calculated by removing the continuous instantaneous linear phase from sample sequence in S 204   c.    
   In a case where zero cross sampler  43  is provided between continuous phase converting unit  28  and linear phase evaluator  29 , sample sequence of the continuous instantaneous phase is calculated by approximate zero sampling of the continuous instantaneous phase calculated in S 204   a . In S 204   b , the continuous instantaneous linear phase is calculated and timing jitter sequence Δφ[n] is calculated by removing the continuous instantaneous linear phase from sample sequence S 204   c.    
   The jitter estimating apparatus and the method of the present invention can be used for estimating jitter of, not only a clock signal of a microprocessor but also a clock signal used for another device or a signal with periodicity such as a sine wave signal, as the tested signal. The jitter estimating method described in each embodiment may perform by a program having a module corresponding to each step. The program may be stored in a recording medium and may control the jitter estimating apparatus by reading the program stored in the recording medium and executing the read program with, for example, a computer. 
   According to the present invention, a worst value of jitter can be estimated precisely in extreme short time. Probability in which the peak jitter and peak-to-peak exceed a prescribed value of such as the peak value and the peak-to-peak value can be calculated. 
   Although the present invention has been described by way of exemplary embodiment, the scope of the present invention is not limited to the foregoing embodiment. Various modifications in the foregoing embodiment may be made when the present invention defined in the appended claims is enforced. It is obvious from the definition of the appended claims that embodiments with such modifications also belong to the scope of the present invention.