# 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. – Marcus Müller May 6 at 22:03
• So is asking help with homework off the line? or just generally against the rules? – Nyquist-er May 6 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! – Marcus Müller May 6 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. – Nyquist-er May 6 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! – Envidia May 6 at 22:11