impinvar (Signal Processing Toolbox)

Impulse invariance method of 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.

[bz,az] = impinvar(b,a)

uses the default value of 1 Hz for Fs.

[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 will consider nearby poles to be repeated. 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.

Example

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`	Bilinear transformation method of analog-to-digital filter conversion.
`lp2bp`	Lowpass to bandpass analog filter transformation.
`lp2bs`	Lowpass to bandstop analog filter transformation.
`lp2hp`	Lowpass to highpass analog filter transformation.
`lp2lp`	Lowpass to lowpass analog filter transformation.

References

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

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