1
$\begingroup$

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. enter image description here

can someone help me from here I am stuck.

Thanks

$\endgroup$
2
$\begingroup$

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.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.