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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 low pass 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!!

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# Cascading LP filter transfer function

Can you offer guidance or do you also need help?

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