Re: Butterworth Filter

"Terry Given" <my_name@xxxxxxxx> schrieb im Newsbeitrag
news:ko4ve.10075$U4.1324857@xxxxxxxxxxxxxxxxxx
> Helmut Sennewald wrote:
>> ----- Original Message -----
>> From: <dhruveenews@xxxxxxxxx>
>> Newsgroups: sci.electronics.design
>> Sent: Thursday, June 23, 2005 12:20 AM
>> Subject: Butterworth Filter
>>
>>
>>
>>>Hello,
>>> I am working on data acquisition. I have collected some EMG data and
>>>now according to the research papers, the EMG data has to be filtered
>>>using 2nd order dual pass butterworth filter with the cut-off frequency
>>>of 40 Hz. What is 'dual pass'? Can anyone elaborate on it.
>>>
>>>thank you
>>
>>
>> Hello Dan,
>>
>> I bet it means run the signal twice through this filter.
>> So it's finally a 4th degree filtering.
>> The trick is to run it backward through the filter in the
>> second pass. This removes nonlinear phase and delay.
>> It can be only done with with digital signal processing.
>>
>> http://www.abdn.ac.uk/~psy359/dept/Papers/obsavoid.pdf
>> "The raw X-, Y- and Z-coordinates
>> of each IRED were digitally filtered by a dual pass through a
>> 2nd-order Butterworth filter with a cut-off frequency of 20 Hz
>> (equivalent to a 4th-order filter with no phase lag and a cut-off
>> of ~16 Hz)."
>>
>> Best regards,
>> Helmut
>
> Hi Helmut,
>
> can you clarify "run it backward" please?
>
> do you mean take N samples, n = 0...(N-1)
>
> and feed through the filter, giving y0...yN-1
>
> Then starting with the last output YN-1 and working backwards to the first
> output Y0, feed them through the same filter to give yy0...yyN-1 ?
>
> So the second pass through the filter is in negative time, hence the phase
> lags cancel.
>
> Cheers
> Terry

Hello Terry,

yes I have exactly tried that. The only thing we additionally need
is reversing the order of the samples after the second run through
the filter. y(N)=y(0), Y(N-1)=y(1), ....
I had a hard time with Scilab to check this, because I had no
experience with it before.
The result has been indeed a filtered signal with zero delay.

The example below runs a stored data sequence two times
through a 4th degree lowpass filter. The second pass
is done with the sequence reversed(last sample first).
The result is a zero delay dual pass 4th order Butterworth filter.

Best regards,
Helmut



Scilab example
--------------
! The for-loops reverse the data sequence.
! fg=0.02*fs fs=10kHz

t=(0:1e-4:0.1);

sigbase=sin(2*%pi*t*50)+0.5*sin(2*%pi*t*150);

signoise=sigbase+0.5*sin(2*pi*t*1100);

[hz]=iir(4,'lp','***', [0.02 0], [0 0]);

y1=rtitr(hz(2),hz(3),signoise);

y2for=rtitr(hz(2),hz(3),y1);

for j=1:1001, y1rev(1,j)=y1(1002-j);end ;

y20rev=rtitr(hz(2),hz(3),y1rev);

for j=1:1001, y2rev(1,j)=y20rev(1002-j);end ;

xbasc
plot2d(t,signoise,style=3);
plot2d(t,sigbase,style=1);
plot2d(t,y2for,style=4);
plot2d(t,y2rev,style=5);


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