Resampling with minimum delay

On Wed, 26 Oct 2011 17:07:56 -0700, Greg Berchin wrote:

> On Oct 26, 6:15&nbsp;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> 
>> The Wiener filter optimizes for least squares. &nbsp;It's very much like the
>> asymptotic solution to a Kalman filter.
> 
> Got it. It's been a long time since I studied them. I have this vague
> memory that a least-squares solution with a Gaussian distribution *is*
> the maximum likelihood solution. I could be mistaken.
> 
>> > PS Tim, are you the same Tim Wescott who occasionally shows up in the
>> > Control Line Stunt Forumhttp://www.stunthanger.com/smf/?
>>
>> Yes -- I don't recall seeing you on there: do you have a nym, or are
>> you just a lurker?
> 
> I visit the site occasionally, but have never registered. In my younger
> days I was capable of the entire AMA Precision Aerobatics pattern
> (though I never competed), but it's been 35 years since I did a
> wingover. To put it into perspective, the last stunt plane that I flew
> was powered by a Fox .35!

I have yet to do the complete pattern, ever.  I was working up to it in 
my late teens, but then college happened, and marriage, and kids, and I 
never got the time until recently to pick up the reins again.  I started 
competing last October, flying the beginner's pattern.  I can do every 
maneuver of the real thing, but haven't put them all together in one 
flight yet.

I might have done one today, but for breaking the plane.  It's a good 
thing I was flying over soft ground.

(To complete my day I was flying a friend's 1/2A Ringmaster on a very 
sick engine and poorly adjusted controls.  The flight involved a lot of 
quick yanks backward on the handle; it ended when I went over backward 
onto my head.  I've never gotten whacked hard enough to see a white flash 
before; I don't think it's necessary to my future happiness to do it ever 
again.  At any rate, when I opened my eyes and looked around my buddies 
were gathered around the plane, making sure that it was in good shape.  
It's a _really good_ thing I was flying over soft ground today.)

-- 
www.wescottdesign.com

Greg Berchin  <gjberchin@charter.net> wrote:

>Since you have the past signal of infinite duration, I suspect that
>the least-squares optimal solution would be an ideal lowpass filter
>applied to the digital signal interpreted as an analog impulse train.
>Tough to implement, though, and not exactly low-delay.

Doesn't this usually come down to being identical to the Lagrangian
interpolator (which is the first approach I would have used).


Steve

On 26 Okt., 18:06, Vladimir Vassilevsky wrote:
> I had to resample a signal with requirement of minimal processing delay.
> So I made a Lagrange polynomial extrapolator to predict the signal on
> the duration of +1 sample into the future. That is straightforward and
> it works good enough for the job.
> However what could be the other options for extrapolation of the Nyquist
> bandlimited signal? What is an optimal solution for this case?

Wouldn't be that _equivalent_ to
- not extrapolating at all
- using a _different_ lowpass filter
?!

(assuming linear extrapolation)

It seems to me that you'd be better off _directly_ designing the
appropriate lowpass filter that suits your needs w.r.t. a low group
delay for your band of interest.

SG