A little question about THD+N

"mnentwig" <mnentwig@elisanet.fi> writes:

> It can be done without windowing, as Randy said. It can also be done with
> windowing, 

To be honest, my response was probably a little knee-jerk. I was
thinking to myself, "Oh my, another abuse of windowing yet again." 
Only in this application, I'll have to back-peddle and agree that,
under certain scenarios at least, windowing makes sense.

Those scenarios are the ones in which there are not a lot of cycles of
signal captured for analysis. My thinking is that if there are a lot
of cycles captured (say, >100000) , then the energy of the main tone
is going to far outweigh any energy in the "splatter" due to
truncation at the ends.  Alternately, as the number of cycles captured
drops, the relative percentage of the splatter goes up and at some
point becomes non-negligible.

Here's an alternate approach (probably already done by someone out there):
"cancel" the tone instead of "notching" it. In other words, given that you
know the frequency f being used for test, estimate the parameters A and theta
in the signal model s = A*sin(2*pi*f*t + theta) to model the signal in the
captured signal+noise, and then subtract out the estimated signal. You probably
would get better results filtering the data prior to estimating the model
parameters, but the filter's amplitude and phase response would have to be
factored back into the actual modeled amplitude and phase.

In practice, windowing may work just about as well and is a lot easier.

Just my $0.02.
-- 
%  Randy Yates                  % "My Shangri-la has gone away, fading like 
%% Fuquay-Varina, NC            %  the Beatles on 'Hey Jude'" 
%%% 919-577-9882                %  
%%%% <yates@ieee.org>           % 'Shangri-La', *A New World Record*, ELO
http://www.digitalsignallabs.com

Randy Yates wrote:
> "mnentwig" <mnentwig@elisanet.fi> writes:
>
>   
>> It can be done without windowing, as Randy said. It can also be done with
>> windowing, 
>>     
> To be honest, my response was probably a little knee-jerk. I was
> thinking to myself, "Oh my, another abuse of windowing yet again." 
> Only in this application, I'll have to back-peddle and agree that,
> under certain scenarios at least, windowing makes sense.
>
> Those scenarios are the ones in which there are not a lot of cycles of
> signal captured for analysis. My thinking is that if there are a lot
> of cycles captured (say, >100000) , then the energy of the main tone
> is going to far outweigh any energy in the "splatter" due to
> truncation at the ends.  Alternately, as the number of cycles captured
> drops, the relative percentage of the splatter goes up and at some
> point becomes non-negligible.
>
> Here's an alternate approach (probably already done by someone out there):
> "cancel" the tone instead of "notching" it. In other words, given that you
> know the frequency f being used for test, estimate the parameters A and theta
> in the signal model s = A*sin(2*pi*f*t + theta) to model the signal in the
> captured signal+noise, and then subtract out the estimated signal. You probably
> would get better results filtering the data prior to estimating the model
> parameters, but the filter's amplitude and phase response would have to be
> factored back into the actual modeled amplitude and phase.
>
> In practice, windowing may work just about as well and is a lot easier.
>
> Just my $0.02.
>   
Thanks to the both of you!

Monday i'll compare the results from my algorithm with audio precision 
equipment.

--

Clyde