It is right to say that the decentralisation is an extension of delegation of authority.
It can be understood with the help of following example:
Example: If CEO delegates some authority to a divisional manager then this is called delegation of authority. If divisional manager delegates his authority further to his subordinate this will be called decentralisation. If the same process is repeated for two divisions then expansion of decentralisation takes place. If this process is implemented on the organisation as a whole then decentralisation will be at its peak.