Digital filters with control of limit cycles

A second order recursive digital filter having a high frequency complex pole arranged to receive an input signal U.sub.n, where n is a sampling interval, comprising:

• means for forming a once delayed version X.sub.n of the output X.sub.n+1 of said filter and a twice delayed version X.sub.n-1 of said output of said filter;
• means for forming the products a.multidot.X.sub.n and b.multidot.X.sub.n-1, where a and b are multiplier coefficients, a being negative;
• means for forming the sum y.sub.n of said products and said input signal U.sub.n ;
• means for truncating y.sub.n to a j-bit word of value p, where p.ltoreq.y<p+k and where k=2.sup.-j ;
• and
• means for selecting the output of said filter X.sub.n+1 as p if
• y.sub.n =p
• or
• X.sub.n-1 <p
• or
• (X.sub.n-1 -1)=p and .vertline.X.sub.n -X.sub.n-1 .vertline..gtoreq.T
• or
• X.sub.n-1 =p and .vertline.X.sub.n -X.sub.n-1 .vertline.<T, or to select X.sub.n+1 =p+1 if
• X.sub.n-1 -1>p
• or
• X.sub.n-1 =p and .vertline.X.sub.n -X.sub.n-1 .vertline..gtoreq.T
• or
• (X.sub.n-1 -1)=p and .vertline.X.sub.n -X.sub.n-1 .vertline.<T,
• where T is a preselected threshold value.

A second order recursive digital filter having a low frequency complex pole arranged to receive an input signal U.sub.n, where n is a sampling interval, comprising:

• means for forming a once delayed version X.sub.n of the output X.sub.n+1 of said filter and a twice delayed version X.sub.n-1 of said output of said filter;
• means for forming the products a.multidot.X.sub.n and b.multidot.X.sub.n-1, where a and b are multiplier coefficients, a being positive;
• means for forming the sum y.sub.n of said products and said input signal U.sub.n ;
• means for truncating y.sub.n to a j-bit word of value p, where p.ltoreq.y<p+k and where k=2.sup.-j ;
• and
• means for selecting the output of said filter X.sub.n+1 as p if
• y.sub.n =p
• or
• X.sub.n-1 <p
• or
• (X.sub.n-1 -1)=p and .vertline.X.sub.n +X.sub.n-1 .vertline..gtoreq.T
• or
• X.sub.n-1 =p and .vertline.X.sub.n +X.sub.n-1 .vertline.<T, or to select X.sub.n+1 =p+l if
• X.sub.n-1 -1>p
• or
• X.sub.n-1 =p and .vertline.X.sub.n +X.sub.n-1 .vertline..gtoreq.T
• or
• (X.sub.n-1 -1)=p and .vertline.X.sub.n +X.sub.n-1 .vertline.<T,
• where T is a preselected threshold value.

In a second order recursive digital filter for providing an output X.sub.n+1 which is the quantized value of

• y.sub.n =a.multidot.X.sub.n +b.multidot.X.sub.n-1 +U.sub.n
• where n is a uniform sampling interval, X.sub.n and X.sub.n-1 are once and twice delayed versions of X.sub.n, respectively, a and b are multiplier coefficients, and U.sub.n is the input to said filter,
• apparatus for eliminating limit cycles in said output for zero, d.c. and period 2 inputs, said apparatus including:
• (a) means for quantizing y.sub.n to a j-bit word of value p, where p<y.sub.n <p+k and k=2.sup.-j, and
• (b) means for selecting X.sub.n+1 as p or p+k as a function of (a) the relative values of X.sub.n-1 and p and (b) the relative values of X.sub.n, X.sub.n-1 and a threshold value T.