GRAPHICAL INTERPRETATION: CURVE FITTING

• What we seek is the value of the slope, not the differentiated signal. This can be directly estimated using the principle of linear regression.
  
  
• We can cast this estimation problem as a curve-fitting problem with some special constraints that result from the signal processing nature of the problem.
  
  
• Consider the estimation problem shown below:
  
• The slope of a signal can be estimated directly using a linear regression approach. More precisely, we are using a least mean square error parameter estimation approach to finding the equation of a line that best approximates the signal.
  
  
• Note that the slope of the line is represented by the parameter a₁ in the equation shown in the figure above. This is the parameter of interest in this analysis.