how to remove such kind of noise

Hi. If x(m) = s(m) + n(m), where n(m) is a noise whose power spectrum
has random magnitudes at a certain frequency and its harmonies (zero-
valued otherwise). I.e. N(f) != 0 only at k*fo (say, fo = 60Hz, k = 1,
2, 3, ...). How can I remove such kind of noise? Thank you.

"Tinwai" <wangthth@gmail.com> wrote in message 
news:6c011d3b-0ef0-4d44-973f-8550018af03c@s12g2000prg.googlegroups.com...
> Hi. If x(m) = s(m) + n(m), where n(m) is a noise whose power spectrum
> has random magnitudes at a certain frequency and its harmonies (zero-
> valued otherwise). I.e. N(f) != 0 only at k*fo (say, fo = 60Hz, k = 1,
> 2, 3, ...). How can I remove such kind of noise? Thank you.

It's interesting that you didn't say anything about s(m) as related to n(m).

So, assuming that they don't overlap in spectral content then you might use 
a comb notch filter to remove n(m).

You still have to decide a few things:
- the bandwidth of n(m) to be removed as it can't have random magnitudes and 
zero bandwidth.
- the time response of the filter - somewhat related to the bandwidth but 
also related to your requirements.

If the bandwidth is large then the time response might be OK.  But, if the 
bandwidth of n(m) is assumed to be small then you might be tempted to design 
a narrow filter which will have poor transient response.

See:
iircomb in Matlab for example.

Fred 

On Jan 3, 3:23 pm, Tinwai <wangt...@gmail.com> wrote:
> Hi. If x(m) = s(m) + n(m), where n(m) is a noise whose power spectrum
> has random magnitudes at a certain frequency and its harmonies (zero-
> valued otherwise). I.e. N(f) != 0 only at k*fo (say, fo = 60Hz, k = 1,
> 2, 3, ...). How can I remove such kind of noise? Thank you.

A filter of the form

1-z^-n

or

1+z^-n

where n is an integer which will depend at what freq your fundamental
is. This n zeros equally spaced around the unit circle and n poles at
zero (ignore those).

Hardy

Tinwai wrote:
> Hi. If x(m) = s(m) + n(m), where n(m) is a noise whose power spectrum
> has random magnitudes at a certain frequency and its harmonies (zero-
> valued otherwise). I.e. N(f) != 0 only at k*fo (say, fo = 60Hz, k = 1,
> 2, 3, ...). How can I remove such kind of noise? Thank you.

Bear in mind that all of the significant harmonics need to be at 
frequencies less than half the sample rate.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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"Jerry Avins" <jya@ieee.org> wrote in message 
news:aI-dnQO0lsFJ4-HanZ2dnUVZ_ozinZ2d@rcn.net...
> Tinwai wrote:
>> Hi. If x(m) = s(m) + n(m), where n(m) is a noise whose power spectrum
>> has random magnitudes at a certain frequency and its harmonies (zero-
>> valued otherwise). I.e. N(f) != 0 only at k*fo (say, fo = 60Hz, k = 1,
>> 2, 3, ...). How can I remove such kind of noise? Thank you.
>
> Bear in mind that all of the significant harmonics need to be at 
> frequencies less than half the sample rate.
>
> Jerry

Yes, and not to be confused with the delays between filter coefficients/taps 
in some filter structures - where the delays may be multiples of the 
sampling interval in order to get repeated/periodic frequency response.

Fred 

On 3 Jan., 06:42, HardySpicer <gyansor...@gmail.com> wrote:
> On Jan 3, 3:23 pm, Tinwai <wangt...@gmail.com> wrote:
>
> > Hi. If x(m) = s(m) + n(m), where n(m) is a noise whose power spectrum
> > has random magnitudes at a certain frequency and its harmonies (zero-
> > valued otherwise). I.e. N(f) != 0 only at k*fo (say, fo = 60Hz, k = 1,
> > 2, 3, ...). How can I remove such kind of noise? Thank you.
>
> A filter of the form
>
> 1-z^-n
>
> or
>
> 1+z^-n
>
> where n is an integer which will depend at what freq your fundamental
> is. This n zeros equally spaced around the unit circle and n poles at
> zero (ignore those).

But you don't know whether the harmonics k*f0 are spaced equally
around the unit circle ...

On Jan 3, 9:13 pm, Andor <andor.bari...@gmail.com> wrote:
> On 3 Jan., 06:42, HardySpicer <gyansor...@gmail.com> wrote:
>
>
>
> > On Jan 3, 3:23 pm, Tinwai <wangt...@gmail.com> wrote:
>
> > > Hi. If x(m) = s(m) + n(m), where n(m) is a noise whose power spectrum
> > > has random magnitudes at a certain frequency and its harmonies (zero-
> > > valued otherwise). I.e. N(f) != 0 only at k*fo (say, fo = 60Hz, k = 1,
> > > 2, 3, ...). How can I remove such kind of noise? Thank you.
>
> > A filter of the form
>
> > 1-z^-n
>
> > or
>
> > 1+z^-n
>
> > where n is an integer which will depend at what freq your fundamental
> > is. This n zeros equally spaced around the unit circle and n poles at
> > zero (ignore those).
>
> But you don't know whether the harmonics k*f0 are spaced equally
> around the unit circle ...

Ok then you will need to do some long division to divide out the zeros
you don't want and multiply by the new ones.


Hardy

On 3 Jan., 23:36, HardySpicer <gyansor...@gmail.com> wrote:
> On Jan 3, 9:13 pm, Andor <andor.bari...@gmail.com> wrote:
>
>
>
>
>
> > On 3 Jan., 06:42, HardySpicer <gyansor...@gmail.com> wrote:
>
> > > On Jan 3, 3:23 pm, Tinwai <wangt...@gmail.com> wrote:
>
> > > > Hi. If x(m) = s(m) + n(m), where n(m) is a noise whose power spectrum
> > > > has random magnitudes at a certain frequency and its harmonies (zero-
> > > > valued otherwise). I.e. N(f) != 0 only at k*fo (say, fo = 60Hz, k = 1,
> > > > 2, 3, ...). How can I remove such kind of noise? Thank you.
>
> > > A filter of the form
>
> > > 1-z^-n
>
> > > or
>
> > > 1+z^-n
>
> > > where n is an integer which will depend at what freq your fundamental
> > > is. This n zeros equally spaced around the unit circle and n poles at
> > > zero (ignore those).
>
> > But you don't know whether the harmonics k*f0 are spaced equally
> > around the unit circle ...
>
> Ok then you will need to do some long division to divide out the zeros
> you don't want and multiply by the new ones.
>
> Hardy

I guess the real question is whether f0 is known. If so, the problem
is a trivial exercise in filter design. If not, it becomes a tedious
exercise in adaptive filter usage, whose success depends on the
autocorrelation of s(m).

Regards,
Andor

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