Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Initial conditions for transposed direct-form II filter implementation

`z`

` = `

filtic(b,a,y,x)

z` = `

filtic(b,a,y)

`z`

finds
the initial conditions, ` = `

filtic(b,a,y,x)`z`

, for the delays in the *transposed direct-form
II* filter implementation given past outputs `y`

and
inputs `x`

. The vectors `b`

and `a`

represent
the numerator and denominator coefficients, respectively, of the filter's
transfer function.

The vectors `x`

and `y`

contain
the most recent input or output first, and oldest input or output
last.

$$\begin{array}{l}x=[x(-1),x(-2),x(-3),\dots ,x(-n)]\\ y=[y(-1),y(-2),y(-3),\dots ,y(-m)]\end{array}$$

where `n`

is `length(b)-1`

(the
numerator order) and `m`

is `length(a)-1`

(the
denominator order). If` length(x)`

is less than `n`

, `filtic`

pads
it with zeros to length `n`

; if `length(y)`

is
less than `m`

, `filtic`

pads it
with zeros to length `m`

. Elements of `x`

beyond `x(n-1)`

and
elements of `y`

beyond `y(m-1)`

are
unnecessary so `filtic`

ignores them.

Output `z`

is a column vector of length equal
to the larger of * n* and

`z`

describes the state of the delays given past inputs `x`

and
past outputs `y`

.`z`

assumes
that the input ` = `

filtic(b,a,y)`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 `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`

.

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

Was this topic helpful?