Hardware-efficient technique for minimizing startup transients in Direct Form II digital filters

A technique for generating initial startup conditions for Direct Form II digital filters is presented. Instead of discarding initial samples due to transients, the approach proposed here is to set the initial conditions of the filter so that they represent steady-state conditions of initial step excitation. The paper supplements the existing methods based on the assumptions that the previous input sequence is a white noise or mirrored signal. The approach is presented in both recursive and matrix notations. The performance is investigated in comparison with existing techniques. An illustrative example of image restoration and possible physical implementation is presented.