When building a high-order Butterworth filter, split into 2nd-order
components, not 4th-order. Instability due to quantization effects has been
observed on real data even with double-precision floating point.
Adds functionality to compute the response of the filter's transfer function at
a given frequency. This uses the Z domain transform. A new test program
zplot_filter (which is compatible with the existing plot_filter) is provided.
Compute the DC gain of the filter (assuming 0 if unstable) and use that to
set the initial conditions of a filter as follows:
x(t<0)=x(0)
y(t<0)=x(0) × dc_gain