Patent ID: 7877219

Claim:
A system for analyzing a signal displaying a non-monotonic transition, comprising: a data retrieving module configured for determining an independent parameter value set [x i ] and a dependent parameter value set [y(x i )] in a transition interval of a waveform curve y(x) of the signal; a computing module configured for: determining an approximation function F(x) of the waveform curve y(x) according to the independent parameter value set [x i ] and the dependent parameter value set [y(x i )], and determining a first discrete value set [F′(x i )] and a second discrete value set [F″(x i )] by determining a first order differential and a second order differential of the optimal approximation function F(x) based on the first parameter value set [x i ]; and a locating module configured for: determining if the first discrete value set [F′(x i )] has one or more zero values, determining if the optimal approximation function F(x) is non-monotonic and determining a peak point (x i ,F(x i )) in the transition interval of the optimal approximation function F(x) according to each zero value, upon the condition that the first discrete value set [F′(x i )] has one or more zero values, determining a curvature radius R of each peak point according to a formula R=|F″(x i )| −1 , determining an independent parameter range [x i −R,x i +R] by regarding each peak point (x i ,F(x i )) as a center, and determining coordinates of each peak point on the waveform curve y(x) by comparing values in the dependent parameter value set [y(x i )] in each independent parameter range [x i −R,x i +R].