A note on least squares fitting of signal waveforms

Mishra, SK (2007): A note on least squares fitting of signal waveforms.

Abstract

Signal waveforms are very fast dampening oscillatory time series composed of exponential functions. The regular least squares fitting techniques are often unstable when used to fit exponential functions to such signal waveforms since such functions are highly correlated. Of late, some attempts have been made to estimate the parameters of such functions by Monte Carlo based search/random walk algorithms. In this study we use the Differential Evaluation based method of least squares to fit the exponential functions and obtain much more accurate results.

• Item Type: MPRA Paper
• Institution: North-Eastern Hill University, Shillong (India)
• Language: English
• Keywords: Signal waveform; exponential functions; Differential Evolution; Global optimization; Nonlinear Least Squares; Monte Carlo; Curve fitting; parameter estimation; Random Walk; Search methods; Fortran
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

· Han, XL, Pozdin, V, Haridass, C and Misra, P (2006) "Monte Carlo Least-Squares Fitting of Experimental Signal Waveforms", Journal of Information & Computational Science, 3(4), pp. 1-7. http://www.physics1.howard.edu/~pmisra/publications/137_ISICS06.pdf · Mishra, SK (2007) “Performance of Differential Evolution Method in Least Squares Fitting of Some Typical Nonlinear Curves”, SSRN http://ssrn.com/abstract=1010508