Signal Processing Toolbox

impinvar

Impulse invariance method for analog-to-digital filter conversion

Syntax

• [bz,az] = impinvar(b,a,fs)
  [bz,az] = impinvar(b,a)
  [bz,az] = impinvar(b,a,fs,tol)
  

Description

[bz,az] = impinvar(b,a,fs) creates a digital filter with numerator and denominator coefficients bz and az, respectively, whose impulse response is equal to the impulse response of the analog filter with coefficients b and a, scaled by 1/fs. If you leave out the argument fs, or specify fs as the empty vector [], it takes the default value of 1 Hz.

[bz,az] = impinvar(b,a,fs,tol) uses the tolerance specified by tol to determine whether poles are repeated. A larger tolerance increases the likelihood that impinvar interprets closely located poles as multiplicities (repeated ones). The default is 0.001, or 0.1% of a pole's magnitude. Note that the accuracy of the pole values is still limited to the accuracy obtainable by the roots function.

Examples

Convert an analog lowpass filter to a digital filter using impinvar with a sampling frequency of 10 Hz:

• [b,a] = butter(4,0.3,'s');
  [bz,az] = impinvar(b,a,10)
  bz =
    1.0e-006 *
     -0.0000    0.1324    0.5192    0.1273         0
  az =
      1.0000   -3.9216    5.7679   -3.7709    0.9246
  

Algorithm

impinvar performs the impulse-invariant method of analog-to-digital transfer function conversion discussed in reference [1]:

1. It finds the partial fraction expansion of the system represented by b and a.
2. It replaces the poles p by the poles exp(p/fs).
3. It finds the transfer function coefficients of the system from the residues from step 1 and the poles from step 2.

See Also

bilinear, lp2bp, lp2bs, lp2hp, lp2lp

References

[1] Parks, T.W., and C.S. Burrus, Digital Filter Design, John Wiley & Sons, 1987, pp. 206-209.

ifft2

impz