Chapter 43 — FFT and Signal Processing

Fast Fourier Transform (FFT) algorithms enable efficient frequency‑domain analysis for audio, signal processing, and convolution. This chapter covers Cooley–Tukey radix‑2 FFT, real transforms, windowing, and practical applications.

What You'll Learn

• FFT fundamentals: DFT definition, complexity, and radix‑2 Cooley–Tukey algorithm
• Real‑valued FFT optimizations and bit‑reversal indexing
• Windowing functions (Hamming, Hann, Blackman) for spectral analysis
• Practical patterns: convolution, filtering, spectral power, and inverse transforms
• Performance tuning, cache optimization, and JMH measurement

Use this chapter to implement predictable, efficient frequency‑domain transformations for scientific computing and DSP workloads.