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Z-Transform & DSP System Explorer

Interactive z-plane, discrete time-domain simulation, and digital frequency response.

z-Plane (Complex Plane)

Stability boundary is the Unit Circle (|z| = 1)

Time Domain Response (Discrete y[n])

System Function H(z)

Add poles/zeros to see the transfer function...

DSP Intuition Guide:
Inside Unit Circle: Signal decays (Stable).
Outside Unit Circle: Signal grows infinitely (Unstable).
Angle (θ): Determines the digital frequency of oscillation.
Zeros on Unit Circle: Completely blocks that specific frequency.

Frequency Response |H(e^jω)|

Evaluated strictly along the Unit Circle (0 to π)