Riesz transform

The Riesz transform is a mathematical tool used to analyze signals like sounds or images. It is named after a famous mathematician called Marcel Riesz. Let's say you listen to some music and you want to know what notes are being played. You can use the Riesz transform to zoom in and see what different frequencies are present in the music.

Think of sound waves like waves at the beach - they go up and down. The Riesz transform takes a signal like a sound wave and breaks it up into different parts that go up and down at different rates. Just like how waves can be tall or short, these different parts can be strong or weak.

This can be really helpful for analyzing sounds, because different instruments or voices create different patterns of these different parts. The Riesz transform allows us to identify these patterns and study them further.

But the Riesz transform isn't just for sounds - it can also be used for images. Just like how sounds have different frequencies, images also have different patterns of brightness and color. The Riesz transform can break up an image into different patterns, like edges, corners, or textures. This can help us understand what is happening in the image and how it was made.

Overall, the Riesz transform helps us break a signal into different parts so we can understand it better.