Last Minute Lecture

Polynomials & the Fast Fourier Transform (FFT) Explained | Chapter 30 in Introduction to Algorithms Chapter 30 of Introduction to Algorithms explores the Fast Fourier Transform (FFT) , a groundbreaking algorithm for multiplying polynomials efficiently in Θ(n log n) time. The chapter walks through the transition between coefficient and point-value forms of a polynomial, explains the mathematical role of complex roots of unity, and introduces the convolution theorem that underlies many applications in digital signal processing, image analysis, and algorithm design. Watch the video above for a guided walkthrough of FFT and its applications in algorithmic polynomial operations, and don’t forget to subscribe to Last Minute Lecture for more expert chapter summaries from core textbooks. Polynomial Representations: Coefficient vs Point-Value Form A polynomial can be represented in two forms: Coefficient form: A(x) = a₀ + a₁x + ... + aₙ₋₁xⁿ⁻¹ — efficient for evaluation ...