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.
Reply by Biruntha Gnaneswaran●July 18, 20152015-07-18
Hi,
please help me to understand why we need LPC to cepstra conversion ? how its work(steps) ?