# 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! – Marcus Müller Oct 23 '18 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. – Himanshu Sharma Oct 23 '18 at 14:03

## 1 Answer

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.

And yes, you need arrowheads to make this clear.

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 $$z^{-n_{o}} X(z) \leftrightarrow x(n-n_{o})$$. – Himanshu Sharma Oct 23 '18 at 10:28
• If the arrow heads are correct: yes. It's not wrong, but it is inefficient and different from what most text books would show. So unless there good reason to do it your way, I would change it to the "standard" notation. That would potentially save you a lot of extra work and confusion later – Hilmar Oct 23 '18 at 14:06
• Thank you very much. I was expecting this only. – Himanshu Sharma Oct 23 '18 at 15:22