Stability, dynamic range, and roundoff noise in a new second-order recursive digital filter

The limit cycle and roundoff noise behavior of a new second-order digital filter are examined. This digital filter is shown to be free from all constant input limit cycles if magnitude truncation and two's complement arithmetic are used. Low-pass, high-pass, and bandpass transfer functions can be readily obtained by using only two multipliers, two delay elements, and five adders. A closed-form expression of the normalized unit noise gain is derived and compared with the noise gains of other well-known second-order structures.