A new design technique is presented for narrow-band digital notch filters .The transversal filters have linear phase and their design is based on minimization of the integrated error energy over designated approximation bands. The optimal design is formulated as a constrained quadratic programming problem. A closed-from expression for the filter coefficients is presented. The notch frequency and null depth are the tunable parameters and the tuning process is described. It is shown that tuning the filter requires a relatively minimal number of operations, a matrix-vector multiply is required to change the filter coefficients. Several examples are included which show the effectiveness of the proposed design technique.