I am implying that that compressor efficiency is directly related to Ng speed.
Again, yes and no.
As a general rule, compressors are designed to be at their most efficient at their optimum ‘Design Speed’, which is neither at its slowest nor fastest speeds.
Think of a commercial airliner engine. Cruise power is where the engine is designed to be at its most efficient, as this is where the engine will spend the majority of its operation, so ‘Off-Power’ settings below (Taxi) and above (Take-Off) the optimum ‘Design Speed’ would result in reduced efficiency, so faster does not necessarily mean more efficient.
As evidence, modern helicopter gas turbine engines can incorporate VIGV’s and Bleed Valves, so as to prevent stalls and surging during the compressor speed range and having a bleed valve open may well prevent a stall, but it does little for efficiency.
Also, during operation of the VIGV’s or Bleed Valves, the correlation between Wf and Ng is unlikely to be a linear function, due to airflow disturbances and bleeding.