Is it possible to specify number of taps and cutoff frequency independently? When specifying the properties of a moving average filter, is it possible to specify the number of taps and the cutoff frequency?
My guess is no since taps (the number of samples in a moving average filter) is what determines the cutoff frequency according to the frequency response equation.
If I'm wrong, how is it possible to specify the two?
If you talk about a moving average filter then you only have a single degree of freedom, namely the filter length (i.e., the number of taps). Consequently, given the number of taps, the magnitude of the frequency response is fixed and the cut-off frequency is given.
Note that you could also define the delay of the moving average filter as another degree of freedom, but that wouldn't change the filter's magnitude response and its cut-off frequency.
For general FIR filters with $N$ taps you have $N$ degrees of freedom, so you can clearly choose the cut-off frequency independently of the number of taps. But this is not the case for a moving average filter.