# Recursive system

Trying to identify if the system below is recursive or not, I would think a recursive system present output value would depend of a past output and not on a present output value.

Is

$$Y[n] = X[n] - Y[n]$$

a recursive system?

• Do you need past outputs to compute the current output? – Matt L. May 31 '17 at 18:15
• No just the current outputs as feedback to compute current output. – Didi May 31 '17 at 19:06
• Well, then there is no feedback; you can't use the current output to compute the current output, right? – Matt L. May 31 '17 at 20:05

No, it can be rewritten as $y[n] = x[n]/2$. Basically, the output is the input divided by 2...