What the syllabus asks you to cover
Definition of the z -transform, Region of convergence, Relationship to causality. Inverse z-transform, Convolution, Parseval’s theorem’s-transform function H (z) -transient and steady state sinusoidal response, pole -zero relationship stability. Frequency domain sampling and reconstruction, Relationship of the DFT to other transforms. Properties of the Discrete Fourier Transform, Multiplication of two DFTs and Circular Convolution. ( AExE0803)
Start here for the core ideas. A dedicated GitBook topic page was not available; this original guide is introductory. Use the syllabus checklist and references below to study the remaining details.
Keep the transform and its domain together
The Z-transform of a sequence must be accompanied by its region of convergence. The same algebraic expression can describe different sequences with different regions. For rational causal systems, poles inside the unit circle are required for stability; the unit circle must belong to the region of convergence for the frequency response to exist in the usual sense.
Understand the DFT
An N-point DFT represents a finite block using N frequency bins and an implied periodic extension. Multiplication of two N-point DFTs corresponds to circular convolution. To obtain a linear convolution by DFT multiplication, zero-pad to at least samples for sequence lengths L and M.
Try it
Two sequences of lengths 3 and 4 need at least a 6-point transform for alias-free linear convolution by this method.
Check your understanding
Why does a pole plot alone not identify a sequence? Compare DTFT and DFT. Practise inverse Z-transforms, Parseval relationships and frequency-bin calculations.
Pause and recall
Without looking back, explain the main idea, recall a key definition or formula, and describe when it applies. Include assumptions and units where relevant. Revisit any step you could not explain.