Re: [music-dsp] Clock drift and compensation

[Benny Alexandar]

Hi GM,

My application is to capture an analog sine tone  through PC sound card and 
check for discontinuity, glitch, audio gap, attenuation etc.

Please suggest any other reliable methods for this analysis.

-ben

From: music-dsp-boun...@music.columbia.edu 
 on behalf of gm 
Sent: Saturday, March 10, 2018 1:20 AM
To: music-dsp@music.columbia.edu
Subject: Re: [music-dsp] Clock drift and compensation


The problem I see is that your sine wave needs to have a precise amplitude for 
the arcsine.
I don't understand your application so I don't know if this is the case.


Am 09.03.2018 um 19:58 schrieb Benny Alexandar:
Hi GM,
Instead of finding Hilbert transform, I tried with just finding the angle 
between samples
of a fixed frequency sine wave.
I tried to create a sine wave of  frequency x[n] = sin ( 2 * pi * 1/4 * n), and 
tried calculating the angle between samples,
it should be 90 degree. This also can be used to detect any discontinuity in 
the signal.
Below is the octave code which I tried.

One cycle of sine wave consists of 4 samples, two +ve and two -ve.

% generate the sine wave of frequency 1/4
for i = 1 : 20
   x(i) = sin( 2 * pi * ( 1 / 4) * i);
end

% find the angle between samples in degrees.
 for i = 1:20
ang(i)  =  asin( x(i) ) * (180 / pi);
 end

% find the absolute difference between angles
for i = 1:20
 diff(i) =  abs( ang( i + 1 ) - ang( i ));
end

% check for discontinuity
for i = 1:20
if (diff(i) != 90)
  disp("discontinuity")
endif
end


Please verify this logic is correct for discontinuity check.

-ben




From: 
music-dsp-boun...@music.columbia.edu
 

 on behalf of gm 
Sent: Monday, January 29, 2018 1:29 AM
To: music-dsp@music.columbia.edu
Subject: Re: [music-dsp] Clock drift and compensation


diff gives you the phase step per sample,
basically the frequency.

However the phase will jump back to zero periodically when the phase exceeds 
360°
(when it wraps around) in this case diff will get you a wrong result.

So you need to "unwrap" the phase or the phase difference, for example:


diff = phase_new - phase_old
if phase_old > Pi and phase_new < Pi then diff += 2Pi

or similar.

Am 28.01.2018 um 17:19 schrieb Benny Alexandar:
Hi GM,

>> HT -> Atan2 -> differenciate -> unwrap
Could you please explain how to find the drift using HT,

HT -> gives real(I) & imaginary (Q) components of real signal
Atan2 -> the phase of an I Q signal
diff-> gives what ?
unwrap ?

-ben



From: 
music-dsp-boun...@music.columbia.edu
 

 on behalf of gm 
Sent: Saturday, January 27, 2018 5:20 PM
To: music-dsp@music.columbia.edu
Subject: Re: [music-dsp] Clock drift and compensation


I don't understand your project at all so not sure if this is helpful,
probably not,
but you can calculate the drift or instantanous frequency of a sine wave
on a per sample basis
using a Hilbert transform
HT -> Atan2 -> differenciate -> unwrap
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Re: [music-dsp] Clock drift and compensation

[Ethan Duni]

Hi ben

You don't need to evaluate the asin() - it's piecewise monotonic and
symmetrical, so you can get the same comparison directly in the signal
domain.

Specifically, notice that x(n) = sin(2*pi*(1/4)*n) = [...0,1,0,-1,...]. So
you get the same result just by checking ( abs( x[n] - x[n-1] ) == 1 )

Ethan

On Fri, Mar 9, 2018 at 10:58 AM, Benny Alexandar 
wrote:

> Hi GM,
> Instead of finding Hilbert transform, I tried with just finding the angle
> between samples
> of a fixed frequency sine wave.
> I tried to create a sine wave of  frequency x[n] = sin ( 2 * pi * 1/4 *
> n), and tried calculating the angle between samples,
> it should be 90 degree. This also can be used to detect any discontinuity
> in the signal.
> Below is the octave code which I tried.
>
> One cycle of sine wave consists of 4 samples, two +ve and two -ve.
>
> % generate the sine wave of frequency 1/4
> for i = 1 : 20
>x(i) = sin( 2 * pi * ( 1 / 4) * i);
> end
>
> % find the angle between samples in degrees.
>  for i = 1:20
> ang(i)  =  asin( x(i) ) * (180 / pi);
>  end
>
> % find the absolute difference between angles
> for i = 1:20
>  diff(i) =  abs( ang( i + 1 ) - ang( i ));
> end
>
> % check for discontinuity
> for i = 1:20
> if (diff(i) != 90)
>   disp("discontinuity")
> endif
> end
>
>
> Please verify this logic is correct for discontinuity check.
>
> -ben
>
>
>
> --
> *From:* music-dsp-boun...@music.columbia.edu  columbia.edu> on behalf of gm 
> *Sent:* Monday, January 29, 2018 1:29 AM
>
> *To:* music-dsp@music.columbia.edu
> *Subject:* Re: [music-dsp] Clock drift and compensation
>
>
> diff gives you the phase step per sample,
> basically the frequency.
>
> However the phase will jump back to zero periodically when the phase
> exceeds 360°
> (when it wraps around) in this case diff will get you a wrong result.
>
> So you need to "unwrap" the phase or the phase difference, for example:
>
>
> diff = phase_new - phase_old
> if phase_old > Pi and phase_new < Pi then diff += 2Pi
>
> or similar.
>
> Am 28.01.2018 um 17:19 schrieb Benny Alexandar:
>
> Hi GM,
>
> >> HT -> Atan2 -> differenciate -> unwrap
> Could you please explain how to find the drift using HT,
>
> HT -> gives real(I) & imaginary (Q) components of real signal
> Atan2 -> the phase of an I Q signal
> diff-> gives what ?
> unwrap ?
>
> -ben
>
>
> --
> *From:* music-dsp-boun...@music.columbia.edu  columbia.edu>  on behalf of gm
>  
> *Sent:* Saturday, January 27, 2018 5:20 PM
> *To:* music-dsp@music.columbia.edu
> *Subject:* Re: [music-dsp] Clock drift and compensation
>
>
> I don't understand your project at all so not sure if this is helpful,
> probably not,
> but you can calculate the drift or instantanous frequency of a sine wave
> on a per sample basis
> using a Hilbert transform
> HT -> Atan2 -> differenciate -> unwrap
> ___
> dupswapdrop: music-dsp mailing list
> music-dsp@music.columbia.edu
> https://lists.columbia.edu/mailman/listinfo/music-dsp
>
>
>
> ___
> dupswapdrop: music-dsp mailing list
> music-dsp@music.columbia.edu
> https://lists.columbia.edu/mailman/listinfo/music-dsp
>
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Re: [music-dsp] Clock drift and compensation

[gm]

The problem I see is that your sine wave needs to have a precise 
amplitude for the arcsine.

I don't understand your application so I don't know if this is the case.


Am 09.03.2018 um 19:58 schrieb Benny Alexandar:

Hi GM,
Instead of finding Hilbert transform, I tried with just finding the 
angle between samples

of a fixed frequency sine wave.
I tried to create a sine wave of  frequency x[n] = sin ( 2 * pi * 1/4 
* n), and tried calculating the angle between samples,
it should be 90 degree. This also can be used to detect any 
discontinuity in the signal.

Below is the octave code which I tried.

One cycle of sine wave consists of 4 samples, two +ve and two -ve.

% generate the sine wave of frequency 1/4
for i = 1 : 20
   x(i) = sin( 2 * pi * ( 1 / 4) * i);
end

% find the angle between samples in degrees.
 for i = 1:20
    ang(i)  =  asin( x(i) ) * (180 / pi);
 end

% find the absolute difference between angles
for i = 1:20
 diff(i) =  abs( ang( i + 1 ) - ang( i ));
end

% check for discontinuity
for i = 1:20
if (diff(i) != 90)
  disp("discontinuity")
endif
end


Please verify this logic is correct for discontinuity check.

-ben




*From:* music-dsp-boun...@music.columbia.edu 
 on behalf of gm 


*Sent:* Monday, January 29, 2018 1:29 AM
*To:* music-dsp@music.columbia.edu
*Subject:* Re: [music-dsp] Clock drift and compensation

diff gives you the phase step per sample,
basically the frequency.

However the phase will jump back to zero periodically when the phase 
exceeds 360°

(when it wraps around) in this case diff will get you a wrong result.

So you need to "unwrap" the phase or the phase difference, for example:


diff = phase_new - phase_old
if phase_old > Pi and phase_new < Pi then diff += 2Pi

or similar.


Am 28.01.2018 um 17:19 schrieb Benny Alexandar:

Hi GM,

>> HT -> Atan2 -> differenciate -> unwrap
Could you please explain how to find the drift using HT,

HT -> gives real(I) & imaginary (Q) components of real signal
Atan2 -> the phase of an I Q signal
diff-> gives what ?
unwrap ?

-ben



*From:* music-dsp-boun...@music.columbia.edu 
 
 
 on behalf of gm 
 

*Sent:* Saturday, January 27, 2018 5:20 PM
*To:* music-dsp@music.columbia.edu 
*Subject:* Re: [music-dsp] Clock drift and compensation

I don't understand your project at all so not sure if this is helpful,
probably not,
but you can calculate the drift or instantanous frequency of a sine wave
on a per sample basis
using a Hilbert transform
HT -> Atan2 -> differenciate -> unwrap
___
dupswapdrop: music-dsp mailing list
music-dsp@music.columbia.edu 
https://lists.columbia.edu/mailman/listinfo/music-dsp





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