LPC spectra estimate Options

[hyeewang]

LPC spectra should correspond with the envelope of DFT spectra.

I plot LPC spectra with matlab. The LPC spectra keep the same shape with the envelope of DFT spectra.

But it is larger with a offset than the DFT envelope.

Why? Where it go wrong?

Here is the matlab script which illustrate it.

N = 2560;
[x,fs] = wavread('lpc.wav',N); % any speech signal can be used

p=12;
a = lpc(x,p);

X =fft(x);
X = X(1:N/2+1)';
X = 10*log10(abs(X).^2);

Z = fft(a,N);
Z = 1./Z(1:N/2+1);
Z = 10*log10(abs(Z).^2);

figure;
plot(X');
hold on;
plot(Z,'r');
grid;
offset = 10;
figure;
plot(X+offset);
hold on;
plot(Z,'r');
grid;

[hyeewang]

LPC spectra should correspond with the envelope of DFT spectra.
I plot LPC spectra with matlab. The LPC spectra keep the same shape with the envelope of DFT spectra.
But it is larger with a offset than the DFT envelope.
Why? Where it go wrong?

What you call "LPC spectra" (by which you probably mean the LPC synthesis filter response) is independent of the input signal's level. If I remember correctly Matlab's LPC function can return more than the set of filter coefficients -- one of those return values gives you a hint about the scaling of the input.

Cheers!
SG

Thank you.

Great job.
It must be here that lpc coefficients were scaled. I would confirm it soon.

LPC function in matlab return LPC coefficients and prediction error variance sigma^2. And LPC coefficients lost important signal energy

information.

But I still do not get the exact scale factor from returned value of lpc function.

Cheers

[SebastianG]

What you call "LPC spectra" (by which you probably mean the LPC synthesis filter response) is independent of the input signal's level. If I remember correctly Matlab's LPC function can return more than the set of filter coefficients -- one of those return values gives you a hint about the scaling of the input.

LPC function in matlab return LPC coefficients and prediction error variance sigma^2.

Bingo!

Guess what happens to this sigma^2 if you scale your input by factor two...

Cheers!
SG

[hyeewang]

What you call "LPC spectra" (by which you probably mean the LPC synthesis filter response) is independent of the input signal's level. If I remember correctly Matlab's LPC function can return more than the set of filter coefficients -- one of those return values gives you a hint about the scaling of the input.

LPC function in matlab return LPC coefficients and prediction error variance sigma^2.

Bingo!

Guess what happens to this sigma^2 if you scale your input by factor two...

Cheers!
SG

Thank you.

It cause sigma^2 to rise 4 times by scaling the input by factor two preceding lpc computation,.

but I still can not get the corresponding input signal power from prediction error variance sigma^2.

N = 25600;
[x,fs] = wavread('origsign.wav',N); % any speech signal can be used
y = 2*x;
p=20;
[a,ae] = lpc(x,p);
[b,be] = lpc(y,p);
be/ae

This post has been edited by hyeewang: Feb 9 2009, 06:53

[SebastianG]

but I still can not get the corresponding input signal power from prediction error variance sigma^2.

If you still havn't figured out the details try

Z = fft(a,N);
Z = sqrt(e*N) ./ Z(1:N/2+1); % <--- changed
Z = 10*log10(abs(Z).^2);

instead -- where 'e' is this sigma^2.

Cheers!
SG

[hyeewang]

but I still can not get the corresponding input signal power from prediction error variance sigma^2.

If you still havn't figured out the details try

Z = fft(a,N);
Z = sqrt(e*N) ./ Z(1:N/2+1); % <--- changed
Z = 10*log10(abs(Z).^2);

instead -- where 'e' is this sigma^2.

Cheers!
SG

Thank you.
I follow u and it work well.

But I did not get the principle,. why the multiplication factor is energy,not variance?

According to LPC theory,synthesis filter

H = G./[1-sum(ai.*Z.(-i))],

E(n) = s(n) - sp(n) = G*e(n);

here,E(n) refer to as lpc pediction error, and e(n) refer to as excitation.
s(n) is the input speech,sp(n) is the estimated signal.

Assume the variance of e(n) to be 1.

sum( E(n)*E(n)) = G.^2*sum( e(n)*e(n)) = G.^2* N;

then G^2 = [sum( E(n)*E(n) ) ] ./ N.

It should be variance(power),not energy. Why?

Thank for your teaching.

This post has been edited by hyeewang: Feb 11 2009, 14:11

[SebastianG]

Z = fft(a,N);
Z = sqrt(e*N) ./ Z(1:N/2+1); % <--- changed
Z = 10*log10(abs(Z).^2);

instead -- where 'e' is this sigma^2.

I follow u and it work well.
But I did not get the principle

'a' and 'e' don't depend on the length of your signal (assuming its characteristics don't change over time). But you wanted both curves to match which is why I included 'N' in the scaling.

Also, are you confusing power with energy?

Cheers!
SG

This post has been edited by SebastianG: Feb 11 2009, 10:31

[hyeewang]

Z = fft(a,N);
Z = sqrt(e*N) ./ Z(1:N/2+1); % <--- changed
Z = 10*log10(abs(Z).^2);

instead -- where 'e' is this sigma^2.

I follow u and it work well.
But I did not get the principle

'a' and 'e' don't depend on the length of your signal (assuming its characteristics don't change over time). But you wanted both curves to match which is why I included 'N' in the scaling.

Also, are you confusing power with energy?

Cheers!
SG

Thank you.

Hehe,I used the term power and energy by mistake. shame.


Indeed, Both a and e do not depend on the length of signal.

But You use e*N,and e*N is the speech signal's energy.

And You still did not explain why you use N to multiply the varince e.

Just use the cause of curves matching reason is weak.

[SebastianG]

Indeed, Both a and e do not depend on the length of signal.
But You use e*N,and e*N is the speech signal's energy.

Not exactly. It's the energy of the prediction residual.

And You still did not explain why you use N to multiply the varince e.
Just use the cause of curves matching reason is weak.

How about telling us why this isn't obvious to you?
What else do you expect?

You know, I really don't like writing big articles about this just so you can understand the topic. I value my sparetime. It's not my job to teach you in my sparetime. I'm just giving hints & pointers that are intended to make you think for yourself.

This post has been edited by SebastianG: Feb 11 2009, 17:12