A new technique for initializing digital IIR filters at two frequencies

Single frequency initialization of a second order digital IIR filter will result in forcing the filter to reach the steady state at either the positive or negative notch frequency and forcing the resultant transient frequency response to be nonsymmetrical. This paper deals with a new technique for initializing digital filters at both frequencies and keeping the symmetry in the frequency response. This is achieved by realizing the second order real digital filter by using two complex first order sections. The internal memories of these filters are initially loaded by their steady state values for a given frequency. An initialization processor is used to calculate the steady state values from the first received sample. This resulted in improving the rejection characteristic of the notch filter. The new technique was also extended to complex filters where the steady state characteristic is enforced at two different frequencies in the stop band.