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Cascading filter transfer function

  1. Oct 28, 2013 #1
    Hi All,
    I'm new to this forum. Its been awhile since university, so i've unfortuntely forgotten most of my teachings on transfer functions it seems!

    Basically im trying to design a 3 stage cascading digital filter. I am sampling an AC waveform and need to integrate the signal. I'm getting some DC offset error from pure integration (trapezoidal method), so have decided to use a cascading filter with an adjustable cut-off freq (set just above the current variable AC electrical freq), and gain multiplication to compensate for attenuation and for the integration.

    I have been told that the transfer function for the 3 identical stage filter of a sine would be
    H(s)=[itex]G*(\frac{1}{\tau*s+1})^{3}[/itex]

    Obviously as i am sampling discretely, I need to be in Z domain
    So I think i'd apply tunstin transformation(?) ;

    s=[itex]\frac{2(z-1)}{T(z+1)}[/itex]

    therefore,

    H(Z) = G*[itex](\frac{1}{\tau[\frac{2(z-1)}{T(z+1)}]+1})^{3}[/itex]

    where [itex]\tau [/itex]= cut-off freq, G = gain, T = Δtime

    But from here i'm kinda stuck, and would appreciate any prompting/help in the right direction. I'm guessing i'll need to do partial fractions? I have tried this, but the answer I got I'm fairly sure is wrong as most of the terms are future sample input/outputs (ie y[n+3], x[n+3]). Is perhaps the z term meant to be [itex]z^{-1}[/itex]? For instance, I have seen in MATLAB simulink the trapezoidal transfer function as;

    [itex]\frac{K*Ts(z+1)}{2(z-1)}[/itex]

    whereas i think it should be;

    [itex]\frac{K*Ts(z^{-1}+1)}{2(z^{-1}-1)}[/itex]

    Perhaps MATLAB uses geophysical(?) definition?

    Perhaps also instead of tunstin transformation, i should just use [itex]s=z^{-1}[/itex]??

    Thanks for any help in advance!!
     
  2. jcsd
  3. Oct 29, 2013 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    Maybe move this to Elec Eng subforum.
     
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