The z-TransformLaplace for discrete time, with the unit circle as its stability boundary.Electrical EngineeringThe z-transform does for discrete-time systemswhat the Laplace transform does for continuousones.X(z) = Σ x[n] z⁻ⁿ · z = exp(sT)One-sample delayz⁻¹The basic block.Pole inside the circleStable|z| < 1.aⁿ u[n]z/(z − a)For |z| > |a|.THE COMMON MISTAKETesting discrete stability in the left half planeTesting it against the unit circleThe map z = exp(sT) sends the left half of the s plane to the inside of the unitcircle, so the boundary changes shape entirely.Sampling wraps the frequency axis onto a circle, so a discrete system'sresponse repeats every sampling frequency.The z-Transformlearnposters.com
The z-Transform — printable engineering wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the The z-Transform poster

The rule, 3 worked examples, and the mistake everyone makes.

Sampling wraps the frequency axis onto a circle, so a discrete system's response repeats every sampling frequency.

Questions about the The z-Transform poster

What’s on the The z-Transform poster?
The rule, 3 worked examples, and the mistake everyone makes. The z-transform does for discrete-time systems what the Laplace transform does for co…; X(z) = Σ x[n] z⁻ⁿ · z = exp(sT); One-sample delay = z⁻¹; Pole inside the circle = Stable; aⁿ u[n] = z/(z − a); Common mistake: Testing discrete stability in the left half plane → Testing it agains…. Sampling wraps the frequency axis onto a circle, so a discrete system's response repeats every sampling frequency.
Who is the The z-Transform poster for?
The z-Transform belongs to the Electrical Engineering section rather than to a school year, because engineering is not something one grade owns. Anyone learning signals & systems can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the The z-Transform poster?
Use it once a system is written as a difference equation rather than a differential one. A wall chart earns its place by being glanceable from where the work is happening, so The z-Transform belongs on the wall where that engineering work actually happens, within glancing distance, rather than filed away.
What other posters go with The z-Transform?
Filter Responses, Bode Plots and Convolution sit alongside The z-Transform in the Electrical Engineering section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Filter ResponsesBode PlotsConvolution
Is the The z-Transform poster free to download and print?
Yes. The z-Transform downloads as a free PDF with no account, no email and no watermark, like everything else in the Electrical Engineering section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the The z-Transform poster print at?
The z-Transform is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of The z-Transform loses nothing.Printing guide

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