Recovering data below a high pass cutoff frequency

Started by November 3, 2005
```Is it possible to recover any data and/or information (e.g. trends)
about a signal below the HP cutoff frequency of a system?   System:
Data is band limited by hardware, at the low end by an AC coupled
amplifier (around 1 Hz) and at the high end by a hardware anti-aliasing
filter (around 64 Hz).   Is it possible in software to ascertain any
information about the signal at frequencies below 1 Hz?

Filter theory tells me that there is attenuated signal on either side
of the passband and that depending on the slope of the filter responses
I can process signal a certain distance from the Nyquist frequency.
But are there any actual advanced methods to analyze frequency response
thing that seems like it contradicts basic filter theory.   I'm just
checking with you guys to make sure I'm not missing something
counter-intuitive that may be out there.

Thanks,
Marc

```
```Marc wrote:
> Is it possible to recover any data and/or information (e.g. trends)
> about a signal below the HP cutoff frequency of a system?   System:
> Data is band limited by hardware, at the low end by an AC coupled
> amplifier (around 1 Hz) and at the high end by a hardware anti-aliasing
> filter (around 64 Hz).   Is it possible in software to ascertain any
> information about the signal at frequencies below 1 Hz?

Sure. A simple R-C rolloff is rather gradual. A time constant of .159
sec/radian will be 3 dB down (half power) at 1 Hz, 5 dB down at .5 Hz,
and 20 dB down at .1 Hz. Those attenuations should be easy to recover
from/ 40 dB down at .01 Hz is more problematic.

> Filter theory tells me that there is attenuated signal on either side
> of the passband and that depending on the slope of the filter responses
> I can process signal a certain distance from the Nyquist frequency.

Not after you sample it. The filter is there to prevent aliasing.

> But are there any actual advanced methods to analyze frequency response
> thing that seems like it contradicts basic filter theory.   I'm just
> checking with you guys to make sure I'm not missing something
> counter-intuitive that may be out there.

All you need is gain and freedom from noise. Freedom from noise is the
hard part, but as Stephan Bernsee once wrote, papier ist duldig (paper

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

> All you need is gain and freedom from noise. Freedom from noise is the
> hard part, but as Stephan Bernsee once wrote, papier ist duldig (paper
>

When Germans say "Papier ist geduldig" they often mean "It looks easy on
paper, but once you try to build it that's a different story".

I don't know what signals Marc is looking at but not much is perfectly
linear in the world. Maybe he could see if anything in his passband got
modulated with whatever low frequency he is after. When we did
hydrophone measurements at several MHz with a narrowband system we could
make out slight rumbling noises in the data from trucks rumbling by on a

Regards, Joerg

http://www.analogconsultants.com
```
```Jerry Avins wrote:
> Marc wrote:
> > Is it possible to recover any data and/or information (e.g. trends)
> > about a signal below the HP cutoff frequency of a system?   System:
> > Data is band limited by hardware, at the low end by an AC coupled
> > amplifier (around 1 Hz) and at the high end by a hardware anti-aliasing
> > filter (around 64 Hz).   Is it possible in software to ascertain any
> > information about the signal at frequencies below 1 Hz?
>
> Sure. A simple R-C rolloff is rather gradual. A time constant of .159
> sec/radian will be 3 dB down (half power) at 1 Hz, 5 dB down at .5 Hz,
> and 20 dB down at .1 Hz. Those attenuations should be easy to recover
> from/ 40 dB down at .01 Hz is more problematic.
>
> > Filter theory tells me that there is attenuated signal on either side
> > of the passband and that depending on the slope of the filter responses
> > I can process signal a certain distance from the Nyquist frequency.
>
> Not after you sample it. The filter is there to prevent aliasing.
>
> > But are there any actual advanced methods to analyze frequency response
> > thing that seems like it contradicts basic filter theory.   I'm just
> > checking with you guys to make sure I'm not missing something
> > counter-intuitive that may be out there.
>
> All you need is gain and freedom from noise. Freedom from noise is the
> hard part, but as Stephan Bernsee once wrote, papier ist duldig (paper

Watch out for group delay variation too!

John

```
```"Jerry Avins" schrieb
>
> but as Stephan Bernsee once wrote, papier ist duldig
> (paper is patient-- read "compliant").
>
Papier ist **ge**duldig, nowadays also called
"Powerpoint Engineering"

PS: From www.leo.org I get the translation
"Papier ist geduldig" <=> "paper doesn't blush"

Regards
Martin

```
```Marc wrote:
> Is it possible to recover any data and/or information (e.g. trends)
> about a signal below the HP cutoff frequency of a system?   System:
> Data is band limited by hardware, at the low end by an AC coupled
> amplifier (around 1 Hz) and at the high end by a hardware anti-aliasing
> filter (around 64 Hz).   Is it possible in software to ascertain any
> information about the signal at frequencies below 1 Hz?
>
> Filter theory tells me that there is attenuated signal on either side
> of the passband and that depending on the slope of the filter responses
> I can process signal a certain distance from the Nyquist frequency.
> But are there any actual advanced methods to analyze frequency response
> thing that seems like it contradicts basic filter theory.   I'm just
> checking with you guys to make sure I'm not missing something
> counter-intuitive that may be out there.

It depends on the filter and the sampling. If the filter has zeros in
the stop
band, it is no way you can recover any signal components in/near those
zeros. Even if there are no zeros in the stop band, the signal may have

been lost due to quantization noise, or any noise that may have been
introduced after the signal was filtered.

Such caveats apart, what you need to do is to find the inverse filter
for the HP filter. If the HP filter is minimum phase, such a filter
exists
that is causal and stable. But as others already have said, what
looks straight-forward on paper...

Rune

```
```Thanks a lot for all your replies guys, they were very helpful.
Interesting parallel German paper discussion as well.

Thanks!
Marc

```
```> Papier ist **ge**duldig, nowadays also called
> "Powerpoint Engineering"
>

ROFL!  How true...

Regards, Joerg

http://www.analogconsultants.com
```
```Joerg wrote:

>> All you need is gain and freedom from noise. Freedom from noise is the
>> hard part, but as Stephan Bernsee once wrote, papier ist duldig (paper

> When Germans say "Papier ist geduldig" they often mean "It looks easy on
> paper, but once you try to build it that's a different story".

> I don't know what signals Marc is looking at but not much is perfectly
> linear in the world.

This reminds me of the deconvolution problems for the Hubble space
telescope before they put in the correction mirror.  The error was known
very accurately, and so was the point spread function.  One of the best
cases of deconvolution that I ever heard about.  It worked only on
strong signals without too much noise, though.

-- glen

```