Documentation

filtic

Initial conditions for transposed direct-form II filter implementation

Syntax

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

Description

z = filtic(b,a,y,x)finds the initial conditions,z, for the delays in thetransposed direct-form IIfilter implementation given past outputsyand inputsx. The vectorsbandarepresent the numerator and denominator coefficients, respectively, of the filter's transfer function.

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

x = [ x ( − 1 ) , x ( − 2 ) , x ( − 3 ) , … , x ( − n ) ] y = [ y ( − 1 ) , y ( − 2 ) , y ( − 3 ) , … , y ( − m ) ]

wherenislength(b)-1(the numerator order) andmislength(a)-1(the denominator order). Iflength(x)is less thann,filticpads it with zeros to lengthn; iflength(y)is less thanm,filticpads it with zeros to lengthm. Elements ofxbeyondx(n-1)and elements ofybeyondy(m-1)are unnecessary sofilticignores them.

Outputzis a column vector of length equal to the larger ofnandm.zdescribes the state of the delays given past inputsxand past outputsy.

z = filtic(b,a,y)assumes that the inputxis 0 in the past.

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

n– 1 is the filter order.

filticworks for both real and complex inputs.

Diagnostics

If any of the input argumentsy,x,b, orais not a vector (that is, if any argument is a scalar or array),filticgives the following error message:

Requires vector inputs.

Algorithms

filticperforms a reverse difference equation to obtain the delay statesz.

References

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

See Also

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Introduced before R2006a

Signal Processing Toolbox Documentation
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