Eliminating harmonics from a fft spectrum of discrete time series data

I am currently writing an honours thesis on producing fourier spectrum from
groundwater signals.  I am trying to identify and filter tidal and
atmospheric responses with periods of between 12 hours and a few days.  I
have been using the Tsoft package produced by the Royal Observatory of
Belgium, that is designed for time series data analysis.

I am getting spectrum with the expected peaks at frequencies around 1 and
2 cpd, however the signals also contain what i believe are simply the
harmonics of the fundamental spectral peaks, that is peaks at 3 and 4 cpd.
 Is there any way that I can eliminate these harmonics or prove that they
are indeed simply harmonics?  

Eg. I am also concerned that the energy at 2 cpd is the sum of the
harmonic of the energy at 1 cpd as well energy genuinely representing the
semidiurnal atmospheric ocsillation.

"Tega" <tega.brain@gmail.com> wrote in
news:3b2dnRgqUZs8sGHZnZ2dnUVZ_tednZ2d@giganews.com: 

> I am currently writing an honours thesis on producing fourier spectrum
> from groundwater signals.  I am trying to identify and filter tidal
> and atmospheric responses with periods of between 12 hours and a few
> days.  I have been using the Tsoft package produced by the Royal
> Observatory of Belgium, that is designed for time series data
> analysis. 
> 
> I am getting spectrum with the expected peaks at frequencies around 1
> and 2 cpd, however the signals also contain what i believe are simply
> the harmonics of the fundamental spectral peaks, that is peaks at 3
> and 4 cpd. 
>  Is there any way that I can eliminate these harmonics or prove that
>  they 
> are indeed simply harmonics?  
> 
> Eg. I am also concerned that the energy at 2 cpd is the sum of the
> harmonic of the energy at 1 cpd as well energy genuinely representing
> the semidiurnal atmospheric ocsillation.
> 
> 
> 


The 2cpd could be a harmonic, but not a sum. 

All in all, what you're finding is that modeling is tough when you can't 
do any controls.  There's no way to stop or alter tides, so you can't 
figure out the stuff you're trying to figure out.

Maybe  you can do a similar analysis at some inland location, where tidal 
effects won't be the same??


-- 
Scott
Reverse name to reply

Hi!

> Is there any way that I can eliminate these harmonics or prove that they
> are indeed simply harmonics?

You can proove that they are harmonics by checking their phases.
All harmonics are always in-phase with the fundamental.
One method for that is bicoherence...

Regards!
Atmapuri

Atmapuri wrote:
> Hi!
>
> > Is there any way that I can eliminate these harmonics or prove that they
> > are indeed simply harmonics?
>
> You can proove that they are harmonics by checking their phases.
> All harmonics are always in-phase with the fundamental.

Really?  Why?
That is certainly NOT true in electronics..

Mark

Atmapuri wrote:
> Hi!
> 
>> Is there any way that I can eliminate these harmonics or prove that they
>> are indeed simply harmonics?
> 
> You can proove that they are harmonics by checking their phases.
> All harmonics are always in-phase with the fundamental.
> One method for that is bicoherence...

Counterexamples are easy to produce. Unless the phase response of the 
system is flat, the observed harmonic will have its phase shifted 
relative to the fundamental.

When comparing the phases of signals not at the same frequency, the 
notion of phase needs precise definition.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Hi!

> When comparing the phases of signals not at the same frequency, the notion 
> of phase needs precise definition.

Or of the harmonics. What is your definition of harmonics?

> All harmonics are always in-phase with the fundamental.
>That is certainly NOT true in electronics..

Depends on how you understand in-phase and harmonics...

Regards!
Atmapuri 

Hi!

> Counterexamples are easy to produce. Unless the phase response of the 
> system is flat, the observed harmonic will have its phase shifted relative 
> to the fundamental.

If phi1 is the fundamental and phi2 is the first harmonic:

sin(2*p*f+phi1)*sin(2*pi*(2*f) + phi2) -> phi1 + phi2 will still be a 
constant despite
the shift. Thats what is called "in-phase".

If the phase restriction is removed from the harmonic definition
then any pair of frequencies at any phase could be called a harmonic...:)
Or are only integer factor accepted? You could have two frequencies
at integer factors (1x, 2x), but their sum of phases would be non-constant.
Is that still a harmonic?

Thanks!
Atmapuri 

Atmapuri said the following on 04/09/2006 21:09:
> 
>> Counterexamples are easy to produce. Unless the phase response of the 
>> system is flat, the observed harmonic will have its phase shifted relative 
>> to the fundamental.
> 
> If phi1 is the fundamental and phi2 is the first harmonic:
> 
> sin(2*p*f+phi1)*sin(2*pi*(2*f) + phi2) -> phi1 + phi2 will still be a 
> constant despite
> the shift. Thats what is called "in-phase".

Ummm...
With the expression above, phi1+phi2 will always be constant, given that 
phi1 and phi2 are constants, so I don't think that expression tells us 
anything (especially as it doesn't contain a time variable).


> If the phase restriction is removed from the harmonic definition
> then any pair of frequencies at any phase could be called a harmonic...:)
> Or are only integer factor accepted? You could have two frequencies
> at integer factors (1x, 2x), but their sum of phases would be non-constant.
> Is that still a harmonic?

If we have two sine waves at arbitrary frequencies f1 and f2, their 
phases will constantly drift in and out in relation to each other - they 
aren't constant by any definition that I can think of.

Obviously, the definition of a harmonic is that f2 is some integer 
multiple of f1.  In such cases, the period of f1 is some integer 
multiple of the "period" of the drift pattern.


-- 
Oli

Dear all, 

Thank you for your feedback.  This forum for public discussion is
invaluable.

warm regards
Tega

Hi!

> Obviously, the definition of a harmonic is that f2 is some integer
> multiple of f1.  In such cases, the period of f1 is some integer multiple
> of the "period" of the drift pattern.

Thanks. I always thought that the phases of harmonics must
be linked together also... So, if the phase one of one changes
so should the phase of the other... but yes since phase and frequency
are connected, small phase changes are also small frequency
changes and condition for fixed integer frequency factor is enough....

Thanks!
Atmapuri