High Pass Filter Ringing - Time Domain

Hi,

I'm using an off-the-shelf DSP package to apply an FFT-based highpass
filter to a time-domain signal. This causes 'ringing' in the output, where
a sine wave appears from nowhere having the same frequency as the high pass
cut-off frequency. The DSP package does not provide much information about
how the filter works, only that it is FFT-based.

Working solely within the time domain, can anyone suggest what sort of
filter or filter settings I should be using so I don't see the rinning
artifacts?

Many thanks,

John

>Hi,
>
>I'm using an off-the-shelf DSP package to apply an FFT-based highpass
>filter to a time-domain signal. This causes 'ringing' in the output,
where
>a sine wave appears from nowhere having the same frequency as the high
pass
>cut-off frequency. The DSP package does not provide much information
about
>how the filter works, only that it is FFT-based.
>
>Working solely within the time domain, can anyone suggest what sort of
>filter or filter settings I should be using so I don't see the rinning
>artifacts?

"FFT-based" doesn't say very much. It could just apply to a filter design
phase, or it could relate to the real time execution of the filter.

If you have ringing, I expect you are trying to achieve a sharp cutoff with
just a few filter elements. At its heart, time domain filtering is a
resonant process. If you want a sharp cutoff you need to use a few sharply
resonant elements, or a larger number of elements with a more damped
resonance. I think it should be obvious which of those two approaches will
yield the filter with the most ringing issues. Now, how you get from where
you are to where you want to be is going to take a bit more knowledge of
your filter software and how it is controlled.

Steve

On 12 apr, 10:02, "FatScouser" <john.hague@n_o_s_p_a_m.truebit.co.uk>
wrote:
> Hi,
>
> I'm using an off-the-shelf DSP package to apply an FFT-based highpass
> filter to a time-domain signal. This causes 'ringing' in the output, where
> a sine wave appears from nowhere having the same frequency as the high pass
> cut-off frequency. The DSP package does not provide much information about
> how the filter works, only that it is FFT-based.
>
> Working solely within the time domain, can anyone suggest what sort of
> filter or filter settings I should be using so I don't see the rinning
> artifacts?

Ringing is part of the filter response. There is nothing
you can do to prevent it from happening.

What remains is to control it so that it stays within
acceptable limits. There are several factors that influence
ringing, like the width of stop-bands, notches and transition
bands.

A lot of amateurs don't understand these things, and write
an FFT-based routine that zeros an arbitrary set of DFT
coefficients. This is a certain way to intropduce these kinds
of artifacts.

To get a working filter,

1) Come up with a specification. Not for what you want (everybody
   want all the benefits without all the drawbacks), but for what
   you need (the benefit you can't do without and the drawbacks
   you can live with).

2) Use a filter design package to find the filter that satisfies
   the spec from 1).

Rune

Hi,

Thanks a lot for your feedback. Specification details include:

1. High-pass filter with cut-off at 0.5 Hz. Cut-off precision is not
critical: a cut-off between 0.2 -> 0.8 Hz is fine.

2. This is a non-realtime calculation, so large computation time is no
problem.

3. A typical signal is a 25 second sample comprising 10000 points sampled
at 400 Hz.

Any help much appreciated!

John

On 12 apr, 10:02, "FatScouser" <john.hague@n_o_s_p_a_m.truebit.co.uk>
>wrote:
>> Hi,
>>
>> I'm using an off-the-shelf DSP package to apply an FFT-based highpass
>> filter to a time-domain signal. This causes 'ringing' in the output,
where
>> a sine wave appears from nowhere having the same frequency as the high
pass
>> cut-off frequency. The DSP package does not provide much information
about
>> how the filter works, only that it is FFT-based.
>>
>> Working solely within the time domain, can anyone suggest what sort of
>> filter or filter settings I should be using so I don't see the rinning
>> artifacts?
>
>Ringing is part of the filter response. There is nothing
>you can do to prevent it from happening.
>
>What remains is to control it so that it stays within
>acceptable limits. There are several factors that influence
>ringing, like the width of stop-bands, notches and transition
>bands.
>
>A lot of amateurs don't understand these things, and write
>an FFT-based routine that zeros an arbitrary set of DFT
>coefficients. This is a certain way to intropduce these kinds
>of artifacts.
>
>To get a working filter,
>
>1) Come up with a specification. Not for what you want (everybody
>   want all the benefits without all the drawbacks), but for what
>   you need (the benefit you can't do without and the drawbacks
>   you can live with).
>
>2) Use a filter design package to find the filter that satisfies
>   the spec from 1).
>
>Rune
>

On 12 apr, 11:46, "FatScouser" <john.hague@n_o_s_p_a_m.truebit.co.uk>
wrote:
> Hi,
>
> Thanks a lot for your feedback. Specification details include:
>
> 1. High-pass filter with cut-off at 0.5 Hz. Cut-off precision is not
> critical: a cut-off between 0.2 -> 0.8 Hz is fine.
>
> 2. This is a non-realtime calculation, so large computation time is no
> problem.
>
> 3. A typical signal is a 25 second sample comprising 10000 points sampled
> at 400 Hz.

There is a lot to be desired here.

How much ripple can you accept in the pass band? What attenuation
at what frequency determines the stop-band?

One needs such information to be able come up with useful answers:

http://www.bores.com/courses/intro/filters/4_spec.htm

Rune

>Hi,
>
>Thanks a lot for your feedback. Specification details include:
>
>1. High-pass filter with cut-off at 0.5 Hz. Cut-off precision is not
>critical: a cut-off between 0.2 -> 0.8 Hz is fine.
>
>2. This is a non-realtime calculation, so large computation time is no
>problem.
>
>3. A typical signal is a 25 second sample comprising 10000 points sampled
>at 400 Hz.
>
>Any help much appreciated!
>
>John

That sounds like your goal is merely to eliminate a DC component. If that
is the case, and you are always working with discrete chunks of some
seconds of data, you'd probably be better off with a 2 pass approach. In
pass 1 you find the average of all the samples. In pass 2 you subtract this
from every sample.

Steve

On Mon, 12 Apr 2010 05:20:50 -0500, "steveu"
<steveu@n_o_s_p_a_m.coppice.org> wrote:

>>Hi,
>>
>>Thanks a lot for your feedback. Specification details include:
>>
>>1. High-pass filter with cut-off at 0.5 Hz. Cut-off precision is not
>>critical: a cut-off between 0.2 -> 0.8 Hz is fine.
>>
>>2. This is a non-realtime calculation, so large computation time is no
>>problem.
>>
>>3. A typical signal is a 25 second sample comprising 10000 points sampled
>>at 400 Hz.
>>
>>Any help much appreciated!
>>
>>John
>
>That sounds like your goal is merely to eliminate a DC component. If that
>is the case, and you are always working with discrete chunks of some
>seconds of data, you'd probably be better off with a 2 pass approach. In
>pass 1 you find the average of all the samples. In pass 2 you subtract this
>from every sample.
>
>Steve

Hello Steve,
  If you are correct about the goal being 
"DC removal", maybe the material at:

http://www.dsprelated.com/showarticle/58.phpFatScouser 

would be useful to FatScouser.

See Ya',
[-Rick-]
   

Hi,

Am afraid I can't give you figures for acceptable passband ripple and
attenuation. All I can say is that I'm using this DSP package to set a
highpass filter at 0.2 Hz, and the output shows a significant ripple at the
same frequency when there is no signal in the input.

Should I apply a Blackman window function as well?

I'm not trying to remove a DC component; I am trying to show the
time-domain signal with frequencies < 0.5 Hz removed.

Sorry I can't be more specific. In terms of relative amplitudes, however,
the resultant ringing artifacts are about 30% of the desired high-frequency
signal.

Thanks,
John

>On Mon, 12 Apr 2010 05:20:50 -0500, "steveu"
><steveu@n_o_s_p_a_m.coppice.org> wrote:
>
>>>Hi,
>>>
>>>Thanks a lot for your feedback. Specification details include:
>>>
>>>1. High-pass filter with cut-off at 0.5 Hz. Cut-off precision is not
>>>critical: a cut-off between 0.2 -> 0.8 Hz is fine.
>>>
>>>2. This is a non-realtime calculation, so large computation time is no
>>>problem.
>>>
>>>3. A typical signal is a 25 second sample comprising 10000 points
sampled
>>>at 400 Hz.
>>>
>>>Any help much appreciated!
>>>
>>>John
>>
>>That sounds like your goal is merely to eliminate a DC component. If
that
>>is the case, and you are always working with discrete chunks of some
>>seconds of data, you'd probably be better off with a 2 pass approach. In
>>pass 1 you find the average of all the samples. In pass 2 you subtract
this
>>from every sample.
>>
>>Steve
>
>Hello Steve,
>  If you are correct about the goal being 
>"DC removal", maybe the material at:
>
>http://www.dsprelated.com/showarticle/58.phpFatScouser 
>
>would be useful to FatScouser.
>
>See Ya',
>[-Rick-]
>   
>

On 12 apr, 14:17, "FatScouser" <john.hague@n_o_s_p_a_m.truebit.co.uk>
wrote:
> Hi,
>
> Am afraid I can't give you figures for acceptable passband ripple and
> attenuation. All I can say is that I'm using this DSP package to set a
> highpass filter at 0.2 Hz, and the output shows a significant ripple at the
> same frequency when there is no signal in the input.

That's related to the impulse response of the filter.
Depending on exactky what you are doing, it might be the
impulse response itself.

Either way, that ringing is related to the narrow bandwidths
mentioned.

> Should I apply a Blackman window function as well?

Not unless you understand why you would want to apply the window.

> I'm not trying to remove a DC component; I am trying to show the
> time-domain signal with frequencies < 0.5 Hz removed.

You shouldn't use the term 'removed'. You should show the signal
with the band *attenuated*. This is not a semantic quibble but
rather the key to obtaining a useful result. As I said previously,
the idea is to not specify a *perfect* solution (which would only
be approximated, causing all kinds of misery and mayhem), but rather
to specify an *acceptable* solution. In order to do that, you
need to specify a lower limit to the pass band.

Or alternatively, re-state the problem as a DC-blocking notch
filter. You might obtain an acceptable result by playing with
notch widths etc.

Rune

FatScouser wrote:
(top posting fixed)
> On 12 apr, 10:02, "FatScouser" <john.hague@n_o_s_p_a_m.truebit.co.uk>
>> wrote:
>>> Hi,
>>>
>>> I'm using an off-the-shelf DSP package to apply an FFT-based highpass
>>> filter to a time-domain signal. This causes 'ringing' in the output,
> where
>>> a sine wave appears from nowhere having the same frequency as the high
> pass
>>> cut-off frequency. The DSP package does not provide much information
> about
>>> how the filter works, only that it is FFT-based.
>>>
>>> Working solely within the time domain, can anyone suggest what sort of
>>> filter or filter settings I should be using so I don't see the rinning
>>> artifacts?
>> Ringing is part of the filter response. There is nothing
>> you can do to prevent it from happening.
>>
>> What remains is to control it so that it stays within
>> acceptable limits. There are several factors that influence
>> ringing, like the width of stop-bands, notches and transition
>> bands.
>>
>> A lot of amateurs don't understand these things, and write
>> an FFT-based routine that zeros an arbitrary set of DFT
>> coefficients. This is a certain way to intropduce these kinds
>> of artifacts.
>>
>> To get a working filter,
>>
>> 1) Come up with a specification. Not for what you want (everybody
>>   want all the benefits without all the drawbacks), but for what
>>   you need (the benefit you can't do without and the drawbacks
>>   you can live with).
>>
>> 2) Use a filter design package to find the filter that satisfies
>>   the spec from 1).
>>
>> Rune
>>
 > Hi,
 >
 > Thanks a lot for your feedback. Specification details include:
 >
 > 1. High-pass filter with cut-off at 0.5 Hz. Cut-off precision is not
 > critical: a cut-off between 0.2 -> 0.8 Hz is fine.
 >
 > 2. This is a non-realtime calculation, so large computation time is no
 > problem.
 >
 > 3. A typical signal is a 25 second sample comprising 10000 points sampled
 > at 400 Hz.
 >
 > Any help much appreciated!

My knee-jerk reaction with this specification would be to try a filter 
with a raised-sine cutoff that starts at 0.2Hz and runs 0.8Hz.  You'll 
get ringing, but it'll be much attenuated over a filter that just hits a 
brick wall at 0.2Hz.

But without knowing the details of your DSP packages I'm not sure if you 
can specify this.

And without knowing what you really need I'm not sure if this will be 
satisfactory.  You can always give it a whirl, and see.

What Rune was trying to point out is that _any_ filter that takes the 
response all the way to zero at any frequency other than DC will suffer 
from ringing to a greater or lesser extent -- you don't get to control 
the existence of ringing, you just get some control over the extent.

If you're filtering distinct chunks of data then windowing the data will 
hold down the spurious high-frequency content and therefore the amount 
of ringing -- but the span over which the windowing function transitions 
from no to full gain will need to be longer than 5 seconds to make much 
difference to a filter that rings at 0.2Hz.

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com