# Let a LTI system be causal and stable with the transfer function being... show that

if the system is an IIR LTI causal and stable one, and the transfer function is

$H(z)=\sum_{n=0}^{\infty}h[n]z{^{n}}= \frac{G}{1 -\sum_{k=1}^{p}a_kz{^{-k}}}$ show that the cepstrum of this system can be calculated by the following equation $\hat{h}[n]= a_n + \sum_{k=1}^{n-1}\left ( \frac{k}{n} \right )\hat{h}[k]a_{n-k}, n\geq 1$ where $\hat{h}[n]=\frac{1}{2\pi}\int_{-\pi}^{\pi}log[H(e{^{j\omega}})]e{^{j\omega n}} d\omega$ is the complex cepstrum. Im basically skipping a lot of parts in defining cepstrum but basically $\hat{H}(z)= log[H(z)]$ Any Ideas what should I look into for answering this question?
• This question appears to be homework. Complete answers to homework are off-topic, but specific questions about homework are acceptable if they include enough detail. Please edit the question to include more background about what you don't understand. May 6, 2021 at 22:03
• So is asking help with homework off the line? or just generally against the rules? May 6, 2021 at 22:05
• asking for help with homework is totally OK, but you need to explain and show what you've tried so far, where that fails, and ask a specific question of your own that helps you find an answer yourself. Your question seems to just repeat the question you are supposed to answer! May 6, 2021 at 22:07
• thanks a ton for replying but I really don't know where I should ask with this one so I thought of asking for hints or some guidance. May 6, 2021 at 22:11
• @poggers100 Even if you don't have any idea how to start, letting us know what you would do or what theory you would apply would get the StackExchange machine going! May 6, 2021 at 22:11