Question regarding filter implementation - Audio EQ Cookbook
With the values you provided ($Q=1$, $f_0=5355\,\text{Hz}$, and $F_s=48\,\text{kHz}$) I get the following filter coefficients from the Cookbook formulas:


b =

   0.11789
   0.23578
   0.11789

a =

   1.32248
  -1.52844
   0.67752


Note that the formulas give you denominator coefficients that are not normalized. Many implementations use $a_0=1$, which can be easily achieved by dividing numerator and denominator coefficients by $a_0=1.32248$.

The maximum pole radius of this filter is $0.72$, which means that we're not at all close to the unit circle, so stability shouldn't be an issue, no matter which implementation you use.

You can add more information if you like, but from what I know up to now, the most likely problem is a bug in your code.

Just test your filtering routine by using as input sequence x=1,0,0,...,, which should give the following output (the impulse response):


ans =

   8.9144e-02
   2.8131e-01
   3.6860e-01
   2.8188e-01
   1.3694e-01
   1.3860e-02
  -5.4140e-02
  -6.9672e-02
  -5.2786e-02
  -2.5313e-02
  -2.2122e-03
   1.0411e-02
   1.3166e-02
   9.8827e-03
   4.6767e-03
   3.4194e-04
  -2.0007e-03
  -2.4875e-03
  -1.8499e-03
  -8.6361e-04
  -5.0389e-05