Transformation between distributions in time-frequency analysis
Alright, let's imagine that you have a bunch of Toy cars, all of them are different colors, and you want to sort them out by colors. You have a blue bin, a red bin, and a green bin, but there are some cars that have more than one color like a blue and red car. So, you need to figure out how to sort those cars too.
This is similar to what happens in time-frequency analysis. You have a bunch of sounds or signals that are made of different frequencies, like a song that has high and low pitches. To study these sounds, scientists analyze how much of each frequency is present at different points in time. Imagine it like a graph that shows the amount of different colors of toy cars you have over time.
But now it gets tricky, because just like some toy cars have two colors, some sounds have frequencies that are not just one clear frequency but are made up of different frequencies mixed together. This is where the transformation between distributions come in, it's like figuring out how to sort the cars that have more than one color.
Scientists use different methods to transform the signal, meaning they change how the frequencies are presented so they can more easily study the signal. Some methods include the Short-Time Fourier Transform, Wavelet Transform, and Continuous Wavelet Transform.
Each method transforms the signal differently, sort of like using different sorting methods for your toy cars. And just like sorting toy cars into bins, different transformations help scientists understand the signal in different ways.
This is similar to what happens in time-frequency analysis. You have a bunch of sounds or signals that are made of different frequencies, like a song that has high and low pitches. To study these sounds, scientists analyze how much of each frequency is present at different points in time. Imagine it like a graph that shows the amount of different colors of toy cars you have over time.
But now it gets tricky, because just like some toy cars have two colors, some sounds have frequencies that are not just one clear frequency but are made up of different frequencies mixed together. This is where the transformation between distributions come in, it's like figuring out how to sort the cars that have more than one color.
Scientists use different methods to transform the signal, meaning they change how the frequencies are presented so they can more easily study the signal. Some methods include the Short-Time Fourier Transform, Wavelet Transform, and Continuous Wavelet Transform.
Each method transforms the signal differently, sort of like using different sorting methods for your toy cars. And just like sorting toy cars into bins, different transformations help scientists understand the signal in different ways.