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This paper proposes an estimation technique in terms of the recursive least-squares (RLS) Wiener filter by operating the wavelet transform to the state vector generating a signal in linear discrete-time stochastic systems. The RLS Wiener filter uses the factorized covariance information of the signal and the variance of observation noise. Here, it is assumed that the observation vector consists of subsequent scalar observed values on the time axis. This paper also examines an estimation technique in terms of the RLS Wiener filter by operating an identity matrix transform to the state vector. It is advantageous that the estimation accuracy by the proposed estimation method is superior to the standard RLS Wiener filter and the estimation procedure with the identity transform matrix.