Optimal matrix filter design with controlled mean-square sidelobe level

In this study, a simple approach for designing a matrix filter with controlled mean-square sidelobe level is proposed. Two methods are used for designing the matrix filter. In design method 1, the authors minimise the normalised mean-square error between the designed and the desired filter responses in the passband subject to the different normalised mean-square error constraints in the left and right stopbands. In design method 2, the objective function and the constraints in the design method 1 are reversed. By using Lagrange multiplier theory, the optimal solution and the optimal value of the optimisations are given, the equations of finding the optimal Lagrange multipliers are offered. In addition, the optimal matrix lowpass filters with symmetric stopband region and equally sidelobe level are given, the matrix codiagonalisation method is used for improving the design efficiency. Numerical results show that the proposed approach is effective for designing matrix filter and filtering short data records.