stmcb (Signal Processing Toolbox)

Linear model using Steiglitz-McBride iteration.

Syntax

[b,a] = stmcb(x,nb,na)
[b,a] = stmcb(x,u,nb,na)
[b,a] = stmcb(x,nb,na,niter)
[b,a] = stmcb(x,u,nb,na,niter)
[b,a] = stmcb(x,nb,na,niter,ai)
[b,a] = stmcb(x,u,nb,na,niter,ai)

Description

Steiglitz-McBride iteration is an algorithm for finding an IIR filter with a prescribed time domain impulse response. It has applications in both filter design and system identification (parametric modeling).

[b,a] = stmcb(x,nb,na)

finds the coefficients b and a of the system b(z)/a(z) with approximate impulse response x, exactly nb zeros, and exactly na poles.

[b,a] = stmcb(x,u,nb,na)

finds the system coefficients b and a of the system that, given u as input, has x as output. x and u must be the same length.

[b,a] = stmcb(x,nb,na,niter)

and

[b,a] = stmcb(x,u,nb,na,niter)

use niter iterations. The default for niter is 5.

[b,a] = stmcb(x,nb,na,niter,ai)

and

[b,a] = stmcb(x,u,nb,na,niter,ai)

use the vector ai as the initial estimate of the denominator coefficients. If ai is not specified, stmcb uses the output argument from [b,ai] = prony(x,0,na) as the vector ai.

stmcb returns the IIR filter coefficients in length nb+1 and na+1 row vectors b and a. The filter coefficients are ordered in descending powers of z:

Example

Approximate the impulse response of a Butterworth filter with a system of lower order:

[b,a] = butter(6,0.2);
h = filter(b,a,[1 zeros(1,100)]);
freqz(b,a,128)



[bb,aa] = stmcb(h,4,4);
freqz(bb,aa,128)

Algorithm

stmcb attempts to minimize the squared error between the impulse response x' of b(z)/a(z) and the input signal x:

stmcb iterates using two steps:

1.: It prefilters x and u using 1/a(z).

2.: It solves a system of linear equations for b and a using \.

stmcb repeats this process niter times. No checking is done to see if the b and a coefficients have converged in fewer than niter iterations.

Diagnostics

If x and u have different lengths, stmcb gives the following error message:

X and U must have same length.

`levinson`	Levinson-Durbin recursion.
`lpc`	Linear prediction coefficients.
`aryule`	Compute an estimate of AR model parameters using the Yule-Walker method.
`prony`	Prony's method for time domain IIR filter design.