From a transfer function to a difference equation

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SMOF
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Hello.

I have been given a transfer function for a digital system, and I need to find the difference equation for that system.

I have attached a pdf with my work. I would be grateful if someone could take a look at it, and see if I am along the right lines.

Thanks in advance, and happy new year to you all.

Seán
 

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I thought I had responded to this before.

You have a typo in your 6th equation, 3rd term on RHS.

Otherwise, I see nothing wrong with your derivation of the differencce equation.
 
Hello,

Thank you very much for the reply!

Yea, I spotted that one a bit after I posted.

Thanks for the feedback! :)

Seán