This podcast dives into convolutions, an essential yet often overlooked operation for combining lists of numbers or functions. It begins with relatable examples from probability, like rolling dice, and then transitions into image processing, showcasing techniques such as blurring and edge detection through engaging visuals. The core idea is simplified using the concept of sliding windows and pairwise products. The discussion wraps up with a powerful convolution algorithm known as FFT, which connects convolutions with polynomial multiplication. This innovative approach can dramatically speed up calculations—by as much as three times in some cases. While this algorithm has the potential to enhance even basic multiplication, its true benefits are best realized with extremely large numbers.
