Robust notch filter design

A technique for designing a notch filter with controlled null width is presented. The basic idea is to minimize the mean square error between the desired unity response and the response of the filter over a frequency band of interest subject to a controlled broad null. Two procedures are proposed for controlling the null width. In one case, the null is controlled to have zero derivatives at the frequency of interest. In the other, a null power constraint over a frequency band of interest is introduced. Numerical techniques based on the matrix factorization method have been proposed for reducing the computational complexity of determining the optimal weight vector for quadratically constrained optimization. Numerical results show that the proposed techniques are very effective in the design of a notch filter with a specified controlled null width and null depth