stmcb

Compute linear model using Steiglitz-McBride iteration

Syntax

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

Description

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

[b,a] = stmcb(h,nb,na)finds the coefficientsbandaof the systemb(z)/a(z) with approximate impulse responseh, exactlynbzeros, and exactlynapoles.

[b,a] = stmcb(y,x,nb,na)finds the system coefficientsbandaof the system that, givenxas input, hasyas output.xandymust be the same length.

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

[b,a] = stmcb(y,x,nb,na,niter)useniteriterations. The default forniteris 5.

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

[b,a] = stmcb(y,x,nb,na,niter,ai)use the vectoraias the initial estimate of the denominator coefficients. Ifai没有指定,stmcbuses the output argument from[b,ai] =prony(h,0,na)as the vectorai.

stmcbreturns the IIR filter coefficients in lengthnb+1andna+1row vectorsbanda. The filter coefficients are ordered in descending powers ofz.

$H (z) = \frac{B (z)}{A (z)} = \frac{b (1) + b (2) z^{- 1} + \dots + b (n b + 1) z^{- n b}}{a (1) + a (2) z^{- 1} + \dots + a (n a + 1) z^{- n a}}$

Examples

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过滤器

Open Live Script

Approximate the impulse response of an IIR filter with a system of lower order.

指定具有标准化3 dB频率的六阶Butterworth滤波器 $0.2 π$ rad/sample.

d = designfilt('lowpassiir','FilterOrder',6,...'HalfPowerFrequency',0.2,'DesignMethod','butter'）；

Use the Steiglitz-McBride iteration to approximate the filter with a 4th-order system.

h = impz(d); [bb,aa] = stmcb(h,4,4);

Plot the frequency responses of the two systems.

hfvt = fvtool(d,bb,aa,'Analysis','freq'）；传奇（hfvt，'Butterworth','Steiglitz-McBride')

Diagnostics

Ifxandyhave different lengths,stmcbproduces this error message:

Input signal X and output signal Y must have the same length.

Algorithms

stmcbattempts to minimize the squared error between the impulse responsehofb(z)/a(z) and the input signalx.

$\min_{a, b} \sum_{i = 0}^{\infty} | x (i) - h (i) |^{2}$

stmcbiterates using two steps:

It prefiltershandx使用1/a(z).
It solves a system of linear equations forbandausing \.

stmcbrepeats this processnitertimes. No checking is done to see if thebandacoefficients have converged in fewer thanniteriterations.

参考

[1] Steiglitz, K., and L. E. McBride. “A Technique for the Identification of Linear Systems.”IEEE^®Transactions on Automatic Control. Vol. AC-10, 1965, pp. 461–464.

[2] Ljung, Lennart.System Identification: Theory for the User. 2nd Edition. Upper Saddle River, NJ: Prentice Hall, 1999, p. 354.

stmcb

Syntax

Description

Examples

过滤器

Diagnostics

Algorithms

参考

See Also

Introduced before R2006a

Signal Processing Toolbox Documentation

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