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References: Fourier Analysis Fundamentals

  1. Fourier series - Wikipedia - Develops periodic-signal expansions, coefficients, convergence, sine-cosine and complex forms, and historical foundations of harmonic analysis.

  2. Fourier transform - Wikipedia - Covers continuous transforms, inverse transforms, key properties, generalized functions, and applications across physics and engineering.

  3. Fast Fourier transform - Wikipedia - Surveys FFT algorithms, Cooley–Tukey factorization, computational complexity, radix choices, and practical transform applications.

  4. The Fourier Transform and Its Applications (3rd Edition) - Ronald N. Bracewell - McGraw-Hill - Bracewell’s pictorial transform pairs and “language of seeing” approach made Fourier duality especially intuitive.

  5. Understanding the FFT: A Tutorial on the Algorithm and Software for Laymen, Students, Technicians and Working Engineers - Anders E. Zonst - Citrus Press - Zonst’s butterfly-by-butterfly numerical walkthrough demystifies FFT computation without hiding implementation details.

  6. Continuous-Time Fourier Transform - Engineering LibreTexts - Derives analysis and synthesis equations from complex exponentials and explains convergence and LTI eigenfunctions.

  7. Signals and Systems - MIT OpenCourseWare - Integrated video lectures, notes, and exercises treat Fourier series, transforms, filtering, sampling, and modulation.

  8. The Scientist and Engineer's Guide to DSP - Steven W. Smith - Presents Fourier decomposition, DFT mechanics, and FFT algorithms through visual, application-oriented explanations and downloadable chapters.

  9. SciPy FFT Documentation - SciPy - Documents executable Fourier, real-transform, multidimensional, and fast-length tools for translating theory into Python experiments.

  10. Spectral Audio Signal Processing - Julius O. Smith III - Offers a free, rigorous bridge from Fourier transforms to spectra, windows, audio analysis, and implementation.