LPC to cepstra conversion

Hi,
please help me to understand why we need LPC to cepstra conversion ? how its work(steps) ?

On Sunday, July 19, 2015 at 3:40:05 AM UTC+12, Biruntha Gnaneswaran wrote:
> Hi,
> please help me to understand why we need LPC to cepstra conversion ? how its work(steps) ?

related to the following - log of a transfer function H(w) ie

ln(H(w) has a power series expansion. The power series coefficients are the ceptstral coefficients

eg try a simple first order transfer function

H(w)= 1/(1+az^-1)

take logs and get

K(z^-1)= -ln(H(w)

=-ln(1+az^-1) = c0 +c1z^-1+c2z^-2 +c3 z^-3+.... and so on

there you have it if you know the formula for ln(1+x)= x+x^/2 + x^3/3+...
so this time at least c0=0

you can extend this to specta by considering

S(w)=abs(H(w))^2X driving white noise power

S(z) = H(z)H(z^-1)X Pin

take logs

ln(S(z))=  ln(H(z) + ln(H(z^-1) + ln (Pin)

and we get a two-sided power series in z with a co term. This is a Laurent series.
It is symmetric about c0. You can easily find the c terms if you know the z transfer function but for more complicated problems this is gonna be a tough algebra!!

Hence we use the  DFT or FFT to extend the idea.