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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)

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    $\begingroup$ "we don't need to take them ..." for what? where? to what end? $\endgroup$
    – Marcus Müller
    Aug 13, 2021 at 13:13
  • $\begingroup$ he just told that and nth more than that. so no idea man. $\endgroup$
    – stackexchangeusername
    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 $\endgroup$
    – stackexchangeusername
    Aug 13, 2021 at 15:57

1 Answer 1

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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

http://www.expertsmind.com/learning/lattice-structure-assignment-help-7342873913.aspx

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.

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  • $\begingroup$ "That negative is important but should go on the other crossover as shown in this picture." I see the same picture as in question. $\endgroup$
    – stackexchangeusername
    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. $\endgroup$
    – stackexchangeusername
    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 $\endgroup$
    – stackexchangeusername
    Aug 14, 2021 at 4:13

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