Everything about Z-transform

🧭 Start here: a 6-step reading path

1. Read the overview: Z-transformA 5-minute orientation
2. Skim a recent paper: Application of Fourier Transform Infrared (FTIR) Spectroscopy in Characterization of Green Synthesized NanoparticlesInfluential work since 2022
3. Pick up a classic book: Anleitung zum praktischen Gebrauch der Laplace-TransformationThe most-reprinted book on the subject
4. Read the landmark paper: Fast and accurate short read alignment with Burrows–Wheeler transformCited 49,626 times
5. Go sideways: Pole–zero plotA closely related topic
6. Go sideways: Minimum phaseA closely related topic

🏆 Landmark papers (most cited)

• Fast and accurate short read alignment with Burrows–Wheeler transform

  Heng Li, Richard Durbin · 2009 · Bioinformatics · 49,626 citations

• MAFFT: a novel method for rapid multiple sequence alignment based on fast Fourier transform

  K. Katoh · 2002 · Nucleic Acids Research · 16,270 citations

• Fast and accurate long-read alignment with Burrows–Wheeler transform

  Heng Li, Richard Durbin · 2010 · Bioinformatics · 11,831 citations

• The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms

  P. Welch · 1967 · IEEE Transactions on Audio and Electroacoustics · 10,996 citations

• Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering

  Kostadin Dabov, Alessandro Foi, Vladimir Katkovnik · 2007 · IEEE Transactions on Image Processing · 8,180 citations

• On the use of windows for harmonic analysis with the discrete Fourier transform

  F.J. Harris · 1978 · Proceedings of the IEEE · 5,924 citations

• Application of the cross wavelet transform and wavelet coherence to geophysical time series

  A. Grinsted, J. C. Moore, S. Jevrejeva · 2004 · Nonlinear Processes in Geophysics · 5,668 citations

• The wavelet transform, time-frequency localization and signal analysis

  I. Daubechies · 1990 · IEEE Transactions on Information Theory · 5,190 citations

🆕 Influential since 2022

• Application of Fourier Transform Infrared (FTIR) Spectroscopy in Characterization of Green Synthesized Nanoparticles

  Sylwia Pasieczna-Patkowska, Marcin Cichy, Jolanta Flieger · 2025 · Molecules · 834 citations

• Lisocabtagene maraleucel versus standard of care with salvage chemotherapy followed by autologous stem cell transplantation as second-line treatment in patients with relapsed or refractory large B-cell lymphoma (TRANSFORM): results from an interim analysis of an open-label, randomised, phase 3 trial

  Manali Kamdar, Scott R Solomon, Jon Arnason · 2022 · The Lancet · 803 citations

• Liquid biopsy: a step closer to transform diagnosis, prognosis and future of cancer treatments

  Saife N. Lone, Sabah Nisar, Tariq Masoodi · 2022 · Molecular Cancer · 794 citations

• Can Large Language Models Transform Computational Social Science?

  Caleb Ziems, William Held, Omar Shaikh · 2024 · Computational Linguistics · 487 citations

• Bond Characterization in Cementitious Material Binders Using Fourier-Transform Infrared Spectroscopy

  Moruf Olalekan Yusuf · 2023 · Applied Sciences · 467 citations

📚 Books worth reading

• Anleitung zum praktischen Gebrauch der Laplace-TransformationGustav Doetsch · 1956
• 📕Wechselströme, drehstrom, leitungen, anwendungen der fourier-, der laplace- und der z-transformationLudwig Brabetz · 2015
• AbtastregelungJ. Ackermann · 1972
• Theory and application of the z-transform methodEliahu Ibrahim Jury · 1964
• Sampled-data control systemsEliahu Ibrahim Jury · 1958
• Applied Laplace Transforms And Z-transforms For Scientists And EngineersUrs Graf · 2004
• 📕Integral Transforms and Fourier SeriesA. N. Srivastava, Mohammad Ahmad · 2012
• Laplace and Z-Transforms (Mathematics for Engineers)W. Bolton · 1997

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• Pole–zero plot In mathematics, signal processing and control theory, a pole–zero plot is a graphical representation of a rational transfer function in the complex plane…
• Minimum phase In control theory and signal processing, a linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable…
• Laplace transform In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable…
• Linear time-invariant system In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal…
• Infinite impulse response Infinite impulse response (IIR) is a fundamental property applying to many linear time-invariant systems that are distinguished by having an impulse response…
• Bilinear transform The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform…
• Two-sided Laplace transform In mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment-generating function…
• Frequency domain In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions…