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Table of contents
Fourier Transforms: Classical Signals to Quantum Circuits
A rigorous undergraduate path from signal spectra and FFTs to the quantum Fourier transform and its algorithms
Read each section in order. Every title can be opened as a TheoryTrace document.
- Cover1
- Copyright2
- How to read this book3
- Introduction4
- Chapter 1: Signals, Systems, and the Spectral Point of View5
- Chapter 2: Mathematical Foundations for Fourier Analysis6
- Chapter 3: Fourier Series for Periodic Continuous-Time Signals7
- Chapter 4: The Continuous-Time Fourier Transform8
- Chapter 5: Fourier Transform Properties and Engineering Use9
- Chapter 6: Impulses, Distributions, and Generalized Fourier Transforms10
- Chapter 7: LTI Systems in the Frequency Domain11
- Chapter 8: Sampling, Aliasing, and Reconstruction12
- Chapter 9: Discrete-Time Fourier Transform13
- Chapter 10: The z-Transform and Its Relation to Fourier Analysis14
- Chapter 11: The Discrete Fourier Transform15
- Chapter 12: Fast Fourier Transform Algorithms16
- Chapter 13: Fourier Methods in Communications and Circuits17
- Chapter 14: Spectral Estimation and Measurement18
- Chapter 15: Linear Algebra View of the DFT19
- Chapter 16: Essentials of Quantum Information for Engineers20
- Chapter 17: Classical Computation, Reversible Logic, and Quantum Circuits21
- Chapter 18: The Quantum Fourier Transform22
- Chapter 19: Quantum Circuit Decomposition of the QFT23
- Chapter 20: Phase Estimation and the Power of the QFT24
- Chapter 21: Quantum Algorithms Based on Fourier Structure25
- Chapter 22: Classical versus Quantum Fourier Transform in Practice26
- Chapter 23: Integrated Projects and Problem-Solving Pathways27
- Chapter 24: Mastery Map and Further Directions28
- Conclusion29