Question

Difference between recursive and nonrecursive system in dsp

Answer 1

A recursive system is a system in which current output depends on previous output(s) and input(s) but in non-recursive system current output does not depend on previous output(s).

The system with memory is not necessarily a recursive system. For example in FIR systems for input x[n] and output y[n] if we have

y[n] = 0.5(x[n]+x[n-1]) then the current output does not depend on previous output but depends on current input and previous input. But for IIR case like an accumulator

y[n] = y[n-1]+x[n], current output is depended on previous output as well as on current input ( generally current and previous inputs). So accumulator is a recursive system.

                 OR                  

A recursive system is a system in which current output depends on previous output(s) and input(s) but in non-recursive system current output does not depend on previous output(s).