# How can I find the Transfer Function in Z-domain?

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?

• Where did the first equation come from? May 24 at 1:01
• 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. May 24 at 1:20