Compute linear model using Steiglitz-McBride iteration
[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)
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(y,x,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(h,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.
Approximate the impulse response of an IIR filter with a system of lower order.
Specify a 6th-order Butterworth filter with normalized 3-dB frequency 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'); legend(hfvt,'Butterworth','Steiglitz-McBride')
If x and y have different lengths, stmcb produces this error message:
Input signal X and output signal Y must have the same length.
stmcb attempts to minimize the squared error between the impulse response h of b(z)/a(z) and the input signal x.
stmcb iterates using two steps:
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.
 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.
 Ljung, Lennart. System Identification: Theory for the User. 2nd Edition. Upper Saddle River, NJ: Prentice Hall, 1999, p. 354.