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Chapter 19

z-Transform

Chapter 19

z-Transform

Definition of z-Transform
The z-transform is a fundamental tool used in analyzing discrete-time systems,  serving as the discrete-time counterpart of the Laplace transform. It …
Region of Convergence
The z-transform converges only for certain values of z. This range of values is known as the Region of Convergence (ROC), which is essential for …
Properties of the z-Transform I
Certain properties provide a solid foundation for analyzing discrete-time systems using the Z-transform. Considering two discrete-time signals, the …
Properties of the z-Transform II
The property of Accumulation is derived by expressing the accumulated sum and applying the time-shifting property to solve for the Z-transform. It states …
Inverse z-Transform by Partial Fraction Expansion
The inverse Z-transform is an essential tool used for converting a function from its frequency domain representation back to the time domain. Consider the …
Difference Equation Solution using z-Transform
Most practical discrete-time systems can be represented by linear difference equations, making the z-transform a particularly useful tool. Knowing the …
Relation of DFT to z-Transform
The Discrete Fourier Transform (DFT) analyzes the frequency content of discrete-time signals. It maps the N-sampled discrete time-domain sequence to its …
High-definition Fourier Transform Infrared (FT-IR) Spectroscopic Imaging of Human Tissue Sections towards Improving Pathology
High-definition Fourier Transform Infrared (FT-IR) spectroscopic imaging is an emerging approach to obtain detailed images that have associated …
Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
The appearance and the movements of immune cells are driven by their environment. As a reaction to a pathogen invasion, the immune cells are recruited to …
Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
Social interaction is of vital importance for human beings. While the hyperscanning approach has been extensively used to study interpersonal neural …