Design method for stable second-order digital filters

The impulse-invariant equivalent digital versions of second-order bandpass analog filters are stable only for coefficients within specific ranges. The quantization of these coefficients may thus cause an originally stable filter to become unstable; the sensitivity of the digital filter to such changes is found to depend on the sampling frequency. Analytic and graphical design techniques are developed for determining the range of sampling frequency that, with a predetermined register length for the coefficients, renders the digital equivalent of a tuned circuit always stable. A comparison is also made between instability caused by quantization of coefficients and limit cycles resulting from the rounding of products.