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?
  • $\begingroup$ 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. $\endgroup$ May 6, 2021 at 22:03
  • $\begingroup$ So is asking help with homework off the line? or just generally against the rules? $\endgroup$
    – Nyquist-er
    May 6, 2021 at 22:05
  • $\begingroup$ 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! $\endgroup$ May 6, 2021 at 22:07
  • $\begingroup$ 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. $\endgroup$
    – Nyquist-er
    May 6, 2021 at 22:11
  • 2
    $\begingroup$ @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! $\endgroup$
    – Envidia
    May 6, 2021 at 22:11


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