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This is my signal;

$y[n]=x[n]+0.8x[n-0.2]$

When I take Z-transform I get;

$Y[z]=X[z]+0.8z^\frac{-1}{5}X[z])$

Then I found the Transfer function as;

$H[z]=\frac{Y[z]}{X[z]}$

$H[z]=1+0.8z^\frac{-1}{5}$

I want to extract the numerator and the denominator parts of this $H[z]$, but all the examples I see have integer z exponentials as -1,-2 etc. How can I save the function from 0.2 exponential?

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  • $\begingroup$ Where did the first equation come from? $\endgroup$ – Pete W May 24 at 1:01
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    $\begingroup$ From my DSP term project. But this complexity is on me. I made a mistake by taking time delay 200ms(0.2s) directly without changing it to sample size. My signal has 44.1kHz sampling frequency and it gives 8820. Thus the initial signal comes as $y[n]=x[n]+0.8x[n-8820]$. Thanks for helping me realize my mistake. $\endgroup$ – talha gungor May 24 at 1:20

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