difference equation block diagram delay or advance confusion

When does the unit delay, become unit advance essentially.

Goal is to deduce difference equation from block diagram. Green text is notes about what the value should be in that node of the diagram.

It appears that the difference equation should be equal to

\begin{align} y[n+2]&=x[n]&-&0.9y[n]\\ x[n]&= 0.9y[n]&+&y[n+2] \end{align}

Green text denotes my personal notes.

1 Answer

It depends from which side of the delay block you look at. Below is an example one sample delay from left to right in the arrow direction :

$$x[n] \longrightarrow \boxed{ z^{-1} } \longrightarrow y[n]$$

Then either $$y[n] = x[n-1]$$ or $$x[n] = y[n+1]$$ are both correct and equivalent expressions.

The first one is written when you trace the delay block in the arrow direction. And you get a delay effect from input x to output y. This is the normal operation direction.

The latter expression is obtained when you trace the delay block in the opposite direction of the arrow. Which gives you an advance effect from signal y to signal x.

• is the answer correct? – Late347 Nov 15 '18 at 22:13
• At the summing node you have $y[n+2] = x[n] - 0.9 y[n]$ and yes the derivation is correct. You can best check this by sending a simple test signal to the system... – Fat32 Nov 15 '18 at 22:31