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.

• Cover
• Copyright
• How to read this book
• Introduction
• Chapter 1: Signals, Systems, and the Spectral Point of View
• Chapter 2: Mathematical Foundations for Fourier Analysis
• Chapter 3: Fourier Series for Periodic Continuous-Time Signals
• Chapter 4: The Continuous-Time Fourier Transform
• Chapter 5: Fourier Transform Properties and Engineering Use
• Chapter 6: Impulses, Distributions, and Generalized Fourier Transforms
• Chapter 7: LTI Systems in the Frequency Domain
• Chapter 8: Sampling, Aliasing, and Reconstruction
• Chapter 9: Discrete-Time Fourier Transform
• Chapter 10: The z-Transform and Its Relation to Fourier Analysis
• Chapter 11: The Discrete Fourier Transform
• Chapter 12: Fast Fourier Transform Algorithms
• Chapter 13: Fourier Methods in Communications and Circuits
• Chapter 14: Spectral Estimation and Measurement
• Chapter 15: Linear Algebra View of the DFT
• Chapter 16: Essentials of Quantum Information for Engineers
• Chapter 17: Classical Computation, Reversible Logic, and Quantum Circuits
• Chapter 18: The Quantum Fourier Transform
• Chapter 19: Quantum Circuit Decomposition of the QFT
• Chapter 20: Phase Estimation and the Power of the QFT
• Chapter 21: Quantum Algorithms Based on Fourier Structure
• Chapter 22: Classical versus Quantum Fourier Transform in Practice
• Chapter 23: Integrated Projects and Problem-Solving Pathways
• Chapter 24: Mastery Map and Further Directions
• Conclusion