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.