The paper is devoted to problem of additive fault estimation observer design for LTI plants with scalar measurement and external disturbance with the known spectral structure. The filter with the calculated parameters should enhance such performances as rapidity of the fault estimation and its insensitivity to the polyharmonical disturbance signal with the certain central frequency, provided by the special filter, generating the corrective signal. The specific spectral approach of H₂ optimization in frequency domain, based on the polynomial factorization, is applied with the aim to improve computational effectiveness of the synthesis. Some theoretical aspects are discussed and numerical algorithm for practical implementation is formulated. Their effectiveness is demonstrated by the numerical example with implementation of MATLAB package.