SGOLAYFILT & Zero Weights: Why the Error in Signal Toolbox?

Why does the SGOLAYFILT function not accept zeros as elements of the weighting vector w, in Signal Processing Toolbox 6.1 (R13+)?

henryjames012 asked: 2020-12-03 matlab , signal , signal processing , SGOLAYFILT function

Understand why MATLABs sgolayfilt function in Signal Processing Toolbox 6.1 (R13) rejects zero values in the weighting vector w. Explore constraints and work

Expert Answer

Kshitij Singh answered . 2025-07-10 21:18:05

This is a weighted least-squares problem. The requirement for the weights to be positive is needed in order to ensure the "least-squares matrix" is positive definite and the system has a solution.

For example, if you change the error checking as suggested above, to allow for zero weights, and try this simple case:

[b,g]=sgolay(3,5,[1,0,0,0,1]);

you will run into matrix singularity issues as indicated by the following warning messages:

 Warning: Matrix is singular to working precision.

 (Type "warning off MATLAB:singularMatrix" to suppress this warning.)

 > In I:\1186207\sgolay.m at line 59

 Warning: Matrix is singular to working precision.

 (Type "warning off MATLAB:singularMatrix" to suppress this warning.)

 > In I:\1186207\sgolay.m at line 59

This is the reason we have this requirement.

You can make some of the weights "very small" if you want to achieve a similar effect as is required here. But it is important to keep in mind that the smaller the weight, the more ill-conditioned the problem will become.

This is due to the so-called inertia theorem for matrices; if

 A = C'*D*C

then A will have the same number of positive eigenvalues as D, the same number of negative eigenvalues, and the same number of zero eigenvalues.

If D (in this case a diagonal matrix with the weights on the diagonal) has a zero eigenvalue (a weight equal to zero in this case), then A will be positive semidefinite (assuming no negative weights) and a solution to the least-squares problem is not guaranteed.

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