Hi Ethan,

This looks interesting. Suppose I have a single tone sound getting mixed with 
audio,
can we find that tone frequency and have an adaptive notch filter ?

Does your above equation works in identifying a fixed frequency tone ?
For example by doing (x(t) + x(t-2)) / (2*x(t-1)) can we isolate a
single tone frequency  ?

-ben

________________________________
From: Ethan Fenn <et...@polyspectral.com>
Sent: Thursday, January 11, 2018 12:13 AM
To: Benny Alexandar
Cc: music-dsp@music.columbia.edu
Subject: Re: [music-dsp] Finding discontinuity in a sine wave.

Well, starting with the FIR filter I proposed, let's take this equality:

0 = x(t) - 2*C*x(t-1) + x(t-2)

If we don't know exactly what our frequency is, we can solve for C:

C = (x(t) + x(t-2)) / (2*x(t-1))

Of course we don't want to take just one computation of C, but if we do some 
averaging and are careful about the singularity when x(t-1) is close to 0, then 
we've got a simple adaptive notch. And we can get a running estimate of the 
frequency by computing arccos(C).

-Ethan



On Wed, Jan 10, 2018 at 12:47 PM, Benny Alexandar 
<ben.a...@outlook.com<mailto:ben.a...@outlook.com>> wrote:
This all works well in an ideal system. Suppose the sampling clock is drifting 
slowly over period of time,
then the notch filter will fail to filter it. How to detect and correct these 
clock drifts and have a stable notch filter.

-ben

________________________________
From: 
music-dsp-boun...@music.columbia.edu<mailto:music-dsp-boun...@music.columbia.edu>
 
<music-dsp-boun...@music.columbia.edu<mailto:music-dsp-boun...@music.columbia.edu>>
 on behalf of Ethan Fenn <et...@polyspectral.com<mailto:et...@polyspectral.com>>
Sent: Wednesday, January 10, 2018 10:33 PM
To: music-dsp@music.columbia.edu<mailto:music-dsp@music.columbia.edu>
Subject: Re: [music-dsp] Finding discontinuity in a sine wave.

If the sine frequency is f and the sample rate is sr:

Let C = cos(2*pi*f/sr)

For each sample compute:

y(t) = x(t) - 2*C*x(t-1) + x(t-2)

y(t) should be 0 for every t... if not it indicates a discontinuity. This is 
just an FIR filter with a zero at the given frequency.

-Ethan




On Wed, Jan 10, 2018 at 11:58 AM, STEFFAN DIEDRICHSEN 
<sdiedrich...@me.com<mailto:sdiedrich...@me.com>> wrote:
With any phase discontinuity, a spectral discontinuity is delivered for free. 
So, the notch filter will have an output, a PPL would need to re-sync, etc.

Steffan


On 10.01.2018|KW2, at 17:51, Benny Alexandar 
<ben.a...@outlook.com<mailto:ben.a...@outlook.com>> wrote:

 But if there is a phase discontinuity it will be hard to detect.



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