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This paper presents an analysis of the constrained least squares filter and a feedback structure is derived which shows the noise cancelling properties of the filter. Using an identification algorithm, it is shown how the constrained least squares filter can be replaced by a finite impulse response filter which can be implemented on-line. The limitations of this F.I.R. filter are discussed. The non-linear behaviour of the constrained least squares (C.L.S.) filter is investigated and, using the proposed feedback structure, it is indicated how a non-linear recursive filter can be identified for on-line implementation.