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Levinson v/s Levinson-Durbin

Started by #ARIJIT BISWAS# ●April 22, 2004
Hi:

I have a doubt:

I know the Levinson-Durbin Algorithm (including the Generalized Levinson-Durbin
Algorithm). Can anyone tell me how does it differ from the previous version,
i.e. the Levinson algorithm?

Since, I don't want to read it, I will be glad if anyone can give me the basic
difference.
Best Regards,

~Arijit




Reply by Andrew Nesterov ●April 23, 20042004-04-23

> Date: Thu, 22 Apr 2004 22:27:42 +0800
> From: "#ARIJIT BISWAS#" <>
>
> Hi:
>
> I have a doubt:
>
> I know the Levinson-Durbin Algorithm (including the Generalized
> Levinson-Durbin Algorithm). Can anyone tell me how does it differ from
> the previous version, i.e. the Levinson algorithm?
>
> Since, I don't want to read it, I will be glad if anyone can give me
> the basic difference.

Arijit,

There seem to be no difference between the two. It is just a matter
of taste and space to say/write Levinson or Levinson-Durbin algorithm.
I don't recall much of the history of the algorithm now, so maybe
someone else more knowledgeble in the history would complement or
correct me.

Regards,
Andrew > Best Regards,
>
> ~Arijit
>

Reply by ●April 23, 20042004-04-23
Dear Arijit,

Quoting from Makhoul's famous 1975 tutorial, for the autocorrelation set
of normal equations
Ra = -r
vector r is unconstrained in Levinson's 1947 work while it's made up of
autocorrelation coefficients in Durbin's 1960 paper. I have not gone
into these originals to check it. Besides, I haven't read anyone else
about this point.

By the way, even Markel and Gray LP Bible call the method just after
Levinson while Rabiner and Schafer in their 1978 best seller call it
just after Durbin. Anyway, most people like you call it Levinson-Durbin
or the other way around.

I would appreciate knowing about the Generalized Levinson-Durbin
algorithm you mentioned at least in its application to speech processing
if at all.

Best regards,
Miguel

#ARIJIT BISWAS# wrote:
>
> Hi:
>
> I have a doubt:
>
> I know the Levinson-Durbin Algorithm (including the Generalized
Levinson-Durbin Algorithm). Can anyone tell me how does it differ from the
previous version, i.e. the Levinson algorithm?
>
> Since, I don't want to read it, I will be glad if anyone can give me the basic
difference.
> Best Regards,
>
> ~Arijit >
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Reply by Shree Jaisimha ●April 23, 20042004-04-23

Dear All,

Does anyone have any sample matlab file for building of a Vector quantization code book of size 256 for speech processing?

If anyone can explain the process with a paper or own explanation would greatly appreciate it.

Thanking you and regards

Shree



Shree Jaisimha


Reply by #ARIJIT BISWAS# ●April 26, 20042004-04-26
Hi Miguel:

Thanks for the information!
The linear equations Ra=-r, have a special property, that the vector on the RHS
also appears as a vector in R.
In the more general case, where the vector on the RHS is some other vector, say
c, the set of linear equations can be solved recursively by introducing a second
recursive equation to solve the more general linear equation Rb=c. The result is
a Generalized Levinson-Durbin Algorithm.

For certain classes of linear predictors (in the warped domain), we need to
solve these general equations!

Best Regards,
~Arijit

-----Original Message-----
From: miguel on behalf of Miguel Arjona Ramez
Sent: Fri 4/23/2004 3:45 PM
To: #ARIJIT BISWAS#
Cc: ;
Subject: Re: [speechcoding] Levinson v/s Levinson-Durbin

Dear Arijit,

Quoting from Makhoul's famous 1975 tutorial, for the autocorrelation set
of normal equations
Ra = -r
vector r is unconstrained in Levinson's 1947 work while it's made up of
autocorrelation coefficients in Durbin's 1960 paper. I have not gone
into these originals to check it. Besides, I haven't read anyone else
about this point.

By the way, even Markel and Gray LP Bible call the method just after
Levinson while Rabiner and Schafer in their 1978 best seller call it
just after Durbin. Anyway, most people like you call it Levinson-Durbin
or the other way around.

I would appreciate knowing about the Generalized Levinson-Durbin
algorithm you mentioned at least in its application to speech processing
if at all.

Best regards,
Miguel

#ARIJIT BISWAS# wrote:
>
> Hi:
>
> I have a doubt:
>
> I know the Levinson-Durbin Algorithm (including the Generalized
Levinson-Durbin Algorithm). Can anyone tell me how does it differ from the
previous version, i.e. the Levinson algorithm?
>
> Since, I don't want to read it, I will be glad if anyone can give me the basic
difference.
> Best Regards,
>
> ~Arijit