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[Erupter]

Hallo.
I've found this old topic and gathered some info about IIR.
I am somewhat familiar with signal theory concepts (convolution, time and frequency domains) as well as with bode, poles and zeros, nyquist.

Now i lack all about digital filters.
I understood the Z transform from what has been said in that topic mentioned above, but when i go and apply it i get totally different results in matlab.
For example i designed this filter

for i=1:k
    for j=1:l
        if((i-j-1) > 0)
            output_vector(1,i)=output_vector(1,i) + (a_vector(1,j)*input_vector(1,i-j-1)) - (b_vector(1,j)*output_vector(1,i-j-1));
        end
    end
end

which should implement an IIR given an input data vector, and two coefficient vectors.
Now if i create the coefficient with

[b,a]=butter(order, wn, 'low');

(i suppose you are familiar with this)
i get an hi-pass instead of a low pass when i put the coeffs in my filter!
I can't begin to understand why.

Also i take that a thing such as this

Y_0 = alpha Y_-1  + (1-alpha) X_0

is a low pass, and it indeed works, but can i get back to a fomulation like

Y/X = 1 / (1 + jw beta)

where beta is somewhat derived from alpha?

Theoretically i've understood the basics, but the fact that in matlab i cannot get predictable behaviour is frustraing to say the least!
I hope you can help me.