There is a common misunderstanding concerning the Doctrine of anatta, saying that through this doctrine Buddha denies the existence of soul. But it is not so, as Buddha denies just the existence of an eternal, unchanging soul, but accepts self/soul as a collection of skandhas, which is not permanent but keeps on changing. He accepts a changing self as an individual ego complex.
Buddhism does not deny the existence of pure self, which is pure consciousness, and only reality. It is termed as BODHI or PRAJNA. He never denied pure conciousness, true aatma or pure self i.e Boddhi or Prajnana.
Upanishads have repeatedly used the term Aatma to symbolize the ultimate reality/transcendental self. Buddha admitted this as Prajna, instead of Aatma and instead relegated the term Aatma to be used in place of Jiva.
Thus, what Buddha calls Aatma is what Jains/Vedantins refer to as Jiva/Buddhi. This is what Buddha emphasizes to be eternally false, which is also accepted by Vedantins/Jains. However, because of this misunderstanding, they condemn each other.
The consciousness/self that is in flux is termed as Chitta by Vedantins, which is a continuous stream with no identity of its own. (Of which Buddha developed KSHANIKAVAD)