On smoothing techniques for the removal of periodic noise of known period

This paper is concerned with the analysis of the linear modely(n)=X(n)+S(n)+(n) for the data sequencey(n) (n=1, 2, ..., N) whereX={x_IJ} is a knownJ × M matrix of full rankM. Here, the(n) are unknown vectors, which we wish to estimate for eachn; S(n) (n=1, 2, ..., N) is a periodic component (which we wish to estimate or remove) superimposed on the linear structureX(n); and(n) is an error vector which is specified as having zero expectation (with possible further properties). Such models commonly occur in geophysical data analysis.Modified from Technical Report No. 33, Computer Centre, The Australian National University.