Initial conditions for transposed direct-form II filter implementation
the initial conditions,
z, for the delays in the transposed direct-form
II filter implementation given past outputs
x. The vectors
the numerator and denominator coefficients, respectively, of the filter's
the most recent input or output first, and oldest input or output
numerator order) and
denominator order). If
length(x) is less than
it with zeros to length
filtic pads it
with zeros to length
m. Elements of
filtic ignores them.
z is a column vector of length equal
to the larger of n and m.
z describes the state of the delays given past inputs
that the input
x is 0 in the past.
The transposed direct-form II structure is shown in the following illustration.
n – 1 is the filter order.
filtic works for both real and complex inputs.
If any of the input arguments
a is not a vector (that is, if any argument
is a scalar or array),
filtic gives the following
Requires vector inputs.
filtic performs a reverse difference equation
to obtain the delay states
 Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, 1989, pp. 296, 301-302.