Z-Transform Properties Explorer
Z-Plane Visualizer
Add Pole
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Add Zero
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ROC Inner Radius
ROC Outer Radius
Property Demonstrator
Linearity
Time-Shifting
Scaling
Linearity Property
Z{ax1(n) + bx2(n)} = aX1(z) + bX2(z)
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Transform Calculator
Custom Signal
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Z-Transform Result
Interactive Learning
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Z-Transform Cheat Sheet
Common Signals
δ(n): 1
u(n): z / (z - 1)
a^n * u(n): z / (z - a)
n * a^n * u(n): az / (z - a)^2
Properties
Linearity: Z{ax(n) + by(n)} = aX(z) + bY(z)
Time-shifting: Z{x(n-k)} = z^(-k)X(z)
Scaling: Z{a^n * x(n)} = X(z/a)
Pro Tip!
The position of poles and zeros in the Z-plane can provide insights into the stability and frequency response of discrete-time systems. Poles inside the unit circle indicate a stable system.
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