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Initial conditions for transposed direct-form II filter implementation

If any of the input arguments `y`

, `x`

,
`b`

, or `a`

is not a vector (that is, if any argument
is a scalar or array), `filtic`

gives the following error message:

Requires vector inputs.

`filtic`

performs a reverse difference equation to obtain the delay
states `z`

. Elements of `x`

beyond `x(n-1)`

and elements of `y`

beyond `y(m-1)`

are unnecessary so
`filtic`

ignores them.

The transposed direct-form II structure is shown in the following illustration.

*n* – 1 is the filter order.

[1] Oppenheim, A.V., and R.W. Schafer,
*Discrete-Time Signal Processing*, Prentice-Hall, 1989, pp. 296,
301-302.