Structure of IIR filter

For the purposes of this library, the following notation is used:

• x(t): value of input function at time t (t = 0, 1, 2, …)
• y(t): value of output at time t
• c[n]: array of x(t) coefficients
• d[n]: array of y(t) coefficients

This leads to a general IIR filter equation:

y(t) = x(t).c[0] + x(t-1).c[1] + … + x(t-N).c[N] - y(t-1).d[0] - y(t-2).d[1] - … - y(t-1-M).d[M]

For initial conditions, the library sets y(t) for t < 0 to x(0).G (where G is the DC gain of the filter, or 0 if it looks like the filter is unstable at DC), and x(t) for t < 0 to x(0).