From the fourier transform of $h[n]=0.5^n u[n]$ ($u[n]$ being unit step function) i've come to find the following equation (using the summation definition for fourier transform):
$${e^{iw} \over e^{iw}-2}$$
From here I am unable to see an easy way to split this up into real and imaginary parts in order to find and sketch the transforms magnitude and phase. Is there an easy way to do this, or even better, an easier way to transform the original $h[n]$ function?
Best Answer
Hint. You may write $$ {e^{iw} \over e^{iw}-2}=\frac{e^{iw}\left(e^{-iw}-2 \right)}{\left(e^{iw}-2\right)\left(e^{-iw}-2\right)} $$then expand the numerator and the denominator.
I hope you can take it from here.