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Zero-Pole Analysis

The zplane function plots poles and zeros of a linear system. For example, a simple filter with a zero at -1/2 and a complex pole pair at 0.9e-j2π0.3 and 0.9ej2π0.3 is

zer = -0.5; 
pol = 0.9*exp(j*2*pi*[-0.3 0.3]');

To view the pole-zero plot for this filter you can use zplane. Supply column vector arguments when the system is in pole-zero form.

zplane(zer,pol)

Figure contains an axes object. The axes object contains 3 objects of type line.

For access to additional tools, use fvtool. First convert the poles and zeros to transfer function form, then call fvtool.

[b,a] = zp2tf(zer,pol,1);
fvtool(b,a)

Figure Filter Visualization Tool - Magnitude Response (dB) contains an axes object and other objects of type uitoolbar, uimenu. The axes object with title Magnitude Response (dB) contains an object of type line.

Click the Pole/Zero Plot toolbar button, select Analysis > Pole/Zero Plot from the menu, or type the following code to see the plot.

fvtool(b,a,'Analysis','polezero')

Figure Filter Visualization Tool - Pole-Zero Plot contains an axes object and other objects of type uitoolbar, uimenu. The axes object with title Pole-Zero Plot contains 3 objects of type line.

To use zplane for a system in transfer function form, supply row vector arguments. In this case, zplane finds the roots of the numerator and denominator using the roots function and plots the resulting zeros and poles.

zplane(b,a)

Figure contains an axes object. The axes object contains 3 objects of type line.

See Discrete-Time System Models for details on zero-pole and transfer function representation of systems.

See Also

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