This is the question

$$ H(z) = \frac{1}{2 + 1.4z^{-1} + 1.8z^{-2}} $$

Lattice structure

My professor has told that we don't need to take those 2 values as negative and instead we can take them as positives(with the same arrow direction). Is he right? What should I do? I am seeing contradicting information on internet vs my professor(My professor doesn't check our final exam paper though)

  • 1
    $\begingroup$ "we don't need to take them ..." for what? where? to what end? $\endgroup$ Aug 13, 2021 at 13:13
  • $\begingroup$ he just told that and nth more than that. so no idea man. $\endgroup$
    – achhainsan
    Aug 13, 2021 at 14:45
  • $\begingroup$ Do you know how to get the lattice coefficients from the transfer function? $\endgroup$
    – Ryan
    Aug 13, 2021 at 14:49
  • $\begingroup$ @Ryan yes for sure i know that $\endgroup$
    – achhainsan
    Aug 13, 2021 at 15:57

1 Answer 1


The reflection coefficients for the system are 1, 0.368, and 0.9.

Based on the recursive difference equations for a lattice filter

$f_{m-1}[n]= f_{m}[n] - K_{m} \times g_{m-1}[n-1]$ $g_{m}[n] = K_{m} \times f_{m-1}[n] + g_{m-1}[n-1]$

That negative is important but should go on the other crossover as shown in this picture.

enter image description here


Bottom line. The negative in that picture should be on the other crossover and you should not “take it as a positive.” Your professor may know something that I don’t about it not mattering in the end, but you will always be right if you keep the negative in your calculations.

EDIT: I changed the picture because the first one I picked was confusing. You can ignore the ladder structure at the bottom since this is an all-pole filter.

  • $\begingroup$ "That negative is important but should go on the other crossover as shown in this picture." I see the same picture as in question. $\endgroup$
    – achhainsan
    Aug 14, 2021 at 2:20
  • $\begingroup$ It is not the same picture as the question. Look closer at the signal flow graph and where the negative is. $\endgroup$
    – Ryan
    Aug 14, 2021 at 2:27
  • $\begingroup$ Both have negative sign in upward arrow, that is what I see. Not sure what you are trying to say. $\endgroup$
    – achhainsan
    Aug 14, 2021 at 2:56
  • $\begingroup$ I found another picture of a block diagram. Can you see it now? It may help to look at the difference equation and try to draw it out yourself. $\endgroup$
    – Ryan
    Aug 14, 2021 at 3:39
  • $\begingroup$ . both have negative sign in upward arrow imgur.com/a/qQjm8rG $\endgroup$
    – achhainsan
    Aug 14, 2021 at 4:13

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