# Block Diagram for a difference equation

I have this little doubt regarding how to draw a block diagram representation of a difference equation. Let us implement $$y(n) = ay(n-3) + by(n-2)+cy(n-1) + x(n)$$ in block diagram where $$a, b, c$$ are constants. What I made is this.

Is this block diagram wrong? They say that you should use only $$z^{-1}$$ delay multiple times to produce the effect of $$z^{-3}$$ and $$z^{-2}$$. But I think that this diagram is also correct. Please help.

• add arrow heads to make this unambiguous! Oct 23, 2018 at 7:30
• I am afraid if it is possible to add arrows now. It is a screenshot. I'll try using GIMP and manually add the arrow. Oct 23, 2018 at 14:03

That's one way to do it but but typically you would have a single line of three delays in the feedback path and apply $$a$$ after the first delay, $$b$$ after the second and $$c$$ after the third.
By convention the coefficient of the feedback path would be called $$a_1$$, $$a_2$$, $$a_3$$ and the feed forward path would be $$b_0$$, $$b_1$$, etc.
• Yeah, I missed the arrows. But my block diagram is correct, right? Since we know that $$z^{-n_{o}} X(z) \leftrightarrow x(n-n_{o})$$. Oct 23, 2018 at 10:28