1. Technical Field
The present invention relates to a probability density function separating apparatus, a probability density function separating method, a program, a testing apparatus, a bit error rate measuring apparatus, an electronic device, and a jitter transfer function measuring apparatus. More particularly, the present invention relates to an apparatus and a method for separating a deterministic component and a random component from a probability density function.
2. Related Art
A method for separating a probability density function with a deterministic component and a probability density function with a random jitter component can be used in an oscilloscope, a time interval analyzer, a universal time frequency counter, automated test equipment, a spectrum analyzer, a network analyzer, and so on. A signal under test may be an electrical signal or an optical signal. The signal under test may indicate information about the variances among products manufactured by the wafer fabrication process.
When amplitude of the signal under test is degraded, a probability by which a reception bit one is erroneously decided to a bit zero is increased. Similarly, when a timing of the signal under test is degraded, a probability of an erroneous decision is increased in proportion to the degradation. It takes longer observation time than Tb/Pe to measure these bit error rates Pe (however, Tb shows a bit rate). As a result, it takes long measurement time to measure an extremely small bit error rate.
For this reason, as measures against amplitude degradation, there has been used a method for setting a bit decision threshold value to a comparatively large value to measure a bit error rate and extrapolate it into an area with an extremely small bit error rate. A deterministic component of a probability density function is bounded and causes a bounded bit error rate. On the other hand, a random component of a probability density function is unbounded. Therefore, a technique for accurately separating a deterministic component and a random component included in measured probability density function and causing bit error rate becomes important.
Conventionally, as a method for separating a deterministic component and a random component included in a probability density function or the like, for example, the invention disclosed in US 2002/0120420 has been known. According to this method, an estimate of variance of a probability density function over a predetermined time interval is computed and the computed estimate of variance is transformed into a frequency domain, in order to determine a random component and a period component constituting the variance. The method uses changing a measured time interval from one cycle to N cycles to measure an autocorrelation function of a period component and an autocorrelation function of a random component and making the Fourier transform respectively correspond to a line spectrum and a white noise spectrum. Here, the variance is a sum of a correlation coefficient of a period component and a correlation coefficient of a random component.
However, a probability density function is given by convolution integrating a deterministic component and a random component. Therefore, according to this method, it is not possible to separate a deterministic component and a random component from a probability density function.
Moreover, as another method for separating a deterministic component and a random component included in a probability density function or the like, for example, the invention disclosed in U.S. Pat. No. 2005/0027477 has been known. As shown in FIG. 2 to be described below, according to this method, both tails of a probability density function are fitted to Gaussian distribution in order to separate two random components from the probability density function. In this method, random components and a deterministic component are performed fit of Gaussian curves under the assumption that both components do not interfere with each other, in order to separate a random component corresponding to Gaussian distribution.
However, it is generally difficult to uniquely determine a boundary between a random component and a deterministic component, and it is difficult to separate a random component with high precision in this method. Moreover, as shown in FIG. 2 to be described below, according to this method, a deterministic component is computed based on a difference D(δδ) between two time instants corresponding to a mean value of each random component.
However, for example, when a deterministic component is a sine wave or the like, it is experimentally confirmed that this difference D(δδ) shows a smaller value than D(p−p) of a true value. In other words, according to this method, since only an ideal deterministic component by a square wave can be approximated, various deterministic components such as a deterministic component of a sine wave are not measured. Furthermore, a measurement error of a random component is also large.