Academic Papers
This bibliography is meant to answer “what is this project standing on?” rather than “what APIs does it expose?”. Use it to place
gpu-fftinside the longer arc of FFT theory, GPU implementation practice, and DSP tooling.
How to read this canon
- Start with the foundational FFT papers if you want the algorithmic lineage.
- Move to the GPU section if you care about memory access, work distribution, and modern accelerator practice.
- Use the DSP and numerical sections to understand why seemingly simple API decisions still have mathematical consequences.
FFT Theory & Algorithms
Foundational Papers
The seminal paper introducing the radix-2 Cooley-Tukey FFT algorithm. This O(n log n) algorithm revolutionized signal processing and remains the foundation of most modern FFT implementations, including this library.
Historical note: Gauss discovered the FFT algorithm decades before Cooley and Tukey, though his work remained obscure until modern times.
Algorithm Variants
Introduced the "Gentleman-Sande" FFT variant (decimation-in-frequency), complementing Cooley-Tukey's decimation-in-time approach.
The split-radix algorithm achieves the lowest known arithmetic complexity for power-of-two sizes: ~4n log₂(n) operations.
Rader's algorithm enables FFT for prime-sized inputs by converting DFT into convolution, achievable via power-of-two FFTs.
Bluestein's chirp z-transform algorithm supports arbitrary-size FFTs through convolution, enabling non-power-of-two transforms.
The prime factor algorithm (PFA) avoids twiddle factors for coprime-sized dimensions, reducing computational overhead.
GPU & Parallel Computing
Comprehensive survey of FFT implementations on GPUs, covering algorithmic adaptations, memory access patterns, and performance optimization strategies.
Industry-standard GPU FFT library. Documentation includes algorithm choices, performance characteristics, and optimization guidelines.
Cross-platform GPU FFT library supporting Vulkan, CUDA, OpenCL, and Metal. Demonstrates advanced optimization techniques for modern GPU architectures.
Foundational work on FFT memory access patterns and optimization for GPU architectures.
Digital Signal Processing
The definitive reference on window functions for spectral analysis. Covers 20+ window types with detailed performance comparisons. This library implements Hann, Hamming, Blackman, and FlatTop windows based on this work.
Standard textbook for DSP. Chapters 8-9 provide comprehensive coverage of DFT theory, FFT algorithms, and spectral analysis.
Another authoritative DSP textbook with detailed coverage of FFT algorithms and their applications.
Classic text with practical insights into FFT implementation and real-world DSP applications.
Numerical Computing
Chapter 5 covers numerical stability of FFT algorithms. Essential reading for understanding floating-point behavior in FFT implementations.
The floating-point standard that governs arithmetic behavior in WebGPU shaders and JavaScript. Understanding IEEE 754 is essential for reasoning about FFT numerical accuracy.
The FFTW paper describes adaptive algorithm selection and code generation techniques that made FFTW the gold standard for CPU FFT performance.
Related Resources
- Reference Implementations - FFT libraries across platforms
- Learning Resources - Tutorials and interactive guides