Doubts regarding dimension of a system:Definitions and algorithms

I need to do phase reconstruction from time series data. In doing so, I encountered Takens' embedding theorem and Cao's minimum embedding dimension $d$ by nearest neighbor method. In paper "Optimal Embeddings of Chaotic Attractors from Topological Considerations" by Liebert et al., 1991, says that minimum embedding dimension for reconstruction should be less than $2m+1$. This confused me since I am aware of Whitney's embedding dimension which stated $d=2*m$ where $m$ is the fractal dimension. Then there is Kennel's method of false nearest neighbor. Can somebody please explain to me:

1. What are the techniques for calculating embedding dimension?


2. Difference between embedding dimension and correlation dimension?


3. What is the technique of proving that a system has finite dimensionality after the signal passes through a filter?


4. Can somebody tell me what is the formula for embedding dimension
   
   
   
   • should it be Cao's method or Kennel's false nearest neighbor method.