combining impluse responses

i have an impluse response that is designed to remove periodicities from a
signal as follows:

h(t) = x(t) - x(t - p)

where p is a period, and for this case p is an integer. i then use
convolution to get a remainder signal with the periodicity removed as so:

z(t) = conv( x(t), h(t) )

i proceed then to get a final filtered signal by extracting the parts of z
from z( p ) to z( max - p ).

This is fine for a single period, but suppose i want to remove two or more
periodicities with one transfer function and one convolution operation?

 i have tried a straight operation of adding the impulse responses without
luck. the reason i want to try multiple impulses for one convolution is
because if i do one period concolution at a time, the remaining signal i can
use gets smaller and smaller. anyone know how to do this?

i have an impluse response that is designed to remove periodicities from a
signal as follows:

h(t) = x(t) - x(t - p)

where p is a period, and for this case p is an integer. i then use
convolution to get a remainder signal with the periodicity removed as so:

z(t) = conv( x(t), h(t) )

i proceed then to get a final filtered signal by extracting the parts of z
from z( p ) to z( max - p ).

This is fine for a single period, but suppose i want to remove two or more
periodicities with one transfer function and one convolution operation?

 i have tried a straight operation of adding the impulse responses without
luck. the reason i want to try multiple impulses for one convolution is
because if i do one period concolution at a time, the remaining signal i can
use gets smaller and smaller. anyone know how to do this?

actually the impluse response is

h(t) = q(t) - q(t - p)

where q(t) is the unit impluse

"Jeremiah Smith" <parlous@hotmail.com> wrote in message
news:vlqf7o20qp4pc3@corp.supernews.com...
>
> i have an impluse response that is designed to remove periodicities from a
> signal as follows:
>
> h(t) = x(t) - x(t - p)
>
> where p is a period, and for this case p is an integer. i then use
> convolution to get a remainder signal with the periodicity removed as so:
>
> z(t) = conv( x(t), h(t) )
>
> i proceed then to get a final filtered signal by extracting the parts of z
> from z( p ) to z( max - p ).
>
> This is fine for a single period, but suppose i want to remove two or more
> periodicities with one transfer function and one convolution operation?
>
>  i have tried a straight operation of adding the impulse responses without
> luck. the reason i want to try multiple impulses for one convolution is
> because if i do one period concolution at a time, the remaining signal i
can
> use gets smaller and smaller. anyone know how to do this?
>
>
>

"Jeremiah Smith" <parlous@hotmail.com> wrote in message news:<vlqf7o20qp4pc3@corp.supernews.com>...
>  i have tried a straight operation of adding the impulse responses without
> luck. the reason i want to try multiple impulses for one convolution is

1. You should concolve, not add impulse responses. 

> because if i do one period concolution at a time, the remaining signal i can
> use gets smaller and smaller. anyone know how to do this?

2. Probably this simple filter is not good enough for narrow notch
filtering: it removes many other frequencies too. You can consider
using narrower notches, e.g. IIR filters.

Alex

"Jeremiah Smith" <parlous@hotmail.com> wrote in message
news:vlqh9fcskoci67@corp.supernews.com...
>
> actually the impluse response is
>
> h(t) = q(t) - q(t - p)
>
> where q(t) is the unit impluse
>
> "Jeremiah Smith" <parlous@hotmail.com> wrote in message
> news:vlqf7o20qp4pc3@corp.supernews.com...
> >
> > i have an impluse response that is designed to remove periodicities from
a
> > signal as follows:
> >
> > h(t) = x(t) - x(t - p)
> >
> > where p is a period, and for this case p is an integer. i then use
> > convolution to get a remainder signal with the periodicity removed as
so:
> >
> > z(t) = conv( x(t), h(t) )
> >
> > i proceed then to get a final filtered signal by extracting the parts of
z
> > from z( p ) to z( max - p ).
> >
> > This is fine for a single period, but suppose i want to remove two or
more
> > periodicities with one transfer function and one convolution operation?
> >
> >  i have tried a straight operation of adding the impulse responses
without
> > luck. the reason i want to try multiple impulses for one convolution is
> > because if i do one period concolution at a time, the remaining signal i
> can
> > use gets smaller and smaller. anyone know how to do this?
>

The impulse response that you offer is defined as the difference between a
function x(t) and itself delayed or advanced in time.  But, you didn't
define x(t).  So that's a problem.  It almost appears that x(t) is a signal.
If x(t) is a signal then the formulation doesn't take into account time
variations of amplitude of the periodic components (and by extension,
phase).

Otherwise, it's not clear what sort of a "system" h(t) represents.  I
suppose "x(t-p)" could be the output of an adapted filter but then it
wouldn't be x(t-p) any more.  The only thing that will generate x(t-p) is a
pure delay.

As suggested, an adapted filter might be a better bet than a pure delay ....
if that's what you meant, it's not at all clear.

Fred

my main goal is to 'filter out' periodicities in a signal mixture. i know
the signal is composed of periodic waveforms, whose waveforms are the same
from period to period. I currently am only concerned with exact integer
periods for simplification.

I can detect one of the present periods reliably, but need to filter the
detected one out to detect the others. You mentioned the use of an IIR
filter - how exactly would it's impluse response look like in formula form?



"Alexey Lukin" <lukin@ixbt.com> wrote in message
news:b225ff4d.0309082159.180f93bd@posting.google.com...
> "Jeremiah Smith" <parlous@hotmail.com> wrote in message
news:<vlqf7o20qp4pc3@corp.supernews.com>...
> >  i have tried a straight operation of adding the impulse responses
without
> > luck. the reason i want to try multiple impulses for one convolution is
>
> 1. You should concolve, not add impulse responses.
>
> > because if i do one period concolution at a time, the remaining signal i
can
> > use gets smaller and smaller. anyone know how to do this?
>
> 2. Probably this simple filter is not good enough for narrow notch
> filtering: it removes many other frequencies too. You can consider
> using narrower notches, e.g. IIR filters.
>
> Alex