Worked Example of a Delay-Free Loop

07 Mar 2012, 12:36 UTC

(If you're not familiar with this kind of diagram, the triangles are scalers/attenuators i.e. multiply-by-constant, the plusses are adders, and the z^-1 boxes are 1-cycle delays.)

From the diagram:

h = x + ay
i = A' = h + bB
y = B' = fi + cA
  = fh + fbB + cA
  = fx + fay + fbB + cA

so

y = (fx + fbB + cA) / (1 - fa)
A' = h + bB
B' = y

In other words,

• y is unchanged from the filter without the delay-free loop, except for the factor 1/(1-fa)
• A' and B' must be calculated using the new y, and using h in place of x

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