Deriving of magnitude, phase response and impulse response of transfer function

Question

I have a transfer function as

$$H(z) = \frac{-0.0625z^4 + 0.25z^3 + 0.625z^2 + 0.25z - 0.0625}{z^4}$$

I want to derive magnitude and phase response of this equation.

can someone help me from here I am stuck.

Thanks

Answer 1

HINT: The frequency response has the form

$$H(e^{j\omega})=a+be^{-j\omega}+ce^{-2j\omega}+be^{-3j\omega}+ae^{-4j\omega}\tag{1}$$

which can be rewritten as

$$H(e^{j\omega})=e^{-2j\omega}\big[ae^{2j\omega}+be^{j\omega}+c+be^{-j\omega}+ae^{-2j\omega}\big]\tag{2}$$

Now note that the term in brackets is purely real-valued. I trust that you can take it from here.