First Order, One Pole filter using the following formula:
y(n) = A0*x(n) - B1*y(n-1)
where y(n) is Output, x(n) is Input and y(n-1) is a delayed copy of the
This filter is a recursive IIR or Infinite Impulse Response filter. It can be
unstable depending on the values of the coefficients. This can be useful as a
low-pass filter, or a "leaky integrator".
A thorough description of the digital filter theory needed to fully describe
this filter is beyond the scope of this document. Calculating coefficients is
non-intuitive; the interested user is referred to one of the standard texts
on filter theory (e.g., Moore, "Elements of Computer Music", section 2.4).