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. enter image description here

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.

  • $\begingroup$ add arrow heads to make this unambiguous! $\endgroup$ Oct 23, 2018 at 7:30
  • $\begingroup$ 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. $\endgroup$ Oct 23, 2018 at 14:03

1 Answer 1


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.

See for example https://www.researchgate.net/figure/Direct-Form-I-structure-of-IIR-filter_fig1_236688224

  • $\begingroup$ Yeah, I missed the arrows. But my block diagram is correct, right? Since we know that $$ z^{-n_{o}} X(z) \leftrightarrow x(n-n_{o}) $$. $\endgroup$ Oct 23, 2018 at 10:28
  • $\begingroup$ 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 $\endgroup$
    – Hilmar
    Oct 23, 2018 at 14:06
  • $\begingroup$ Thank you very much. I was expecting this only. $\endgroup$ Oct 23, 2018 at 15:22

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