17.10 : 快速傅里叶变换

The Fast Fourier Transform, FFT, is a computational algorithm for calculating the Discrete Fourier Transform by breaking the calculations into smaller, manageable sections.

Computing an N-point DFT requires N square complex multiplications, while the FFT algorithm requires only N over two and base two logarithm N multiplications, offering a significantly faster performance.

As N increases, the FFT becomes faster and more efficient by reducing the number of operations from the quadratic to the logarithmic scale.

It uses symmetry and periodicity properties and minimizes redundant calculations and multiplications.

The Inverse Fast Fourier Transform, IFFT, reconstructs the original signal from its frequency-domain representation with enhanced computational efficiency.

Commonly used in signal and image processing, it also plays a vital role in wireless communication, scientific research, and data analysis.