| T O P I C R E V I E W |
| ubitelli@n1 |
Posted - 05/19/2003 : 4:03:11 PM
Hi people.
Regard the last post, I did not find the book Hans suggested but I have foud others books. However I still have questions about the
FFT smooth procedure. If I am not wrong, the procedure is something
like this:
1)Take the FFT of the data.
2)Multiply this FFT by a function (a filter?) that has a value of 1
at zero Hz and 0 at the frequency of 1/(N*dx) where N is the number
of points used to smoothing and dx is the interval in the x axis. In this way, we remove the components above the frequency cutoff of
1/(N*dx).
3)Take the inverse FFT.
Well, in the item 2, are the data above cutoff removed or replaced
by zero? I think they must be replaced because the number of data
points must not change.
Anyway, I used this procedure with simulated
data and my results did not agree with Origin (I didīt use any
function but replaced the data by zero using brute force - with few points it is easy).
What is wrong?
Thanks
Ricardo.
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| 8 L A T E S T R E P L I E S (Newest First) |
| rtoomey |
Posted - 11/14/2005 : 3:27:54 PM
quote:
The cutoff is not a sharp cutoff, which would then be just a low pass filter. Rather it is a parabolic shape that falls off to zero at the cutoff frequency:
http://www.originlab.com/www/products/origin/analysis_fft_filter_smoothing.asp
Are you looking for more information, such as to how this parabola is constructed?
Just to note...the URL above is no longer valid. The new URL is: http://www.originlab.com/index.aspx?s=8&lm=115&pid=78
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| ubitelli@n1 |
Posted - 06/03/2003 : 11:41:32 AM
Hi Easwar
Thanks for your code. I have runned in Origin 6.1 and the results
are slightly different as you said. But now I know how the calculations are done. The "trick" was the negative frequency part
of the spectrum isnīt it?
Thank you.
Ricardo. |
| easwar |
Posted - 05/30/2003 : 4:54:12 PM
Hi Ricardo,
Sorry for the delay in replying.
I presume you are trying to do this using the GUI by doing FFT, then multiplying with filter etc. You need to be careful in doing this because you need to multiply both positive and negative frequencies by the parabolic shape.
Try the LabTalk code posted below.
This code assumes that your time data is in data1_a, and the signal data is in data1_b.
Running the script will then create FFT1 and IFFT1 worksheets.
It will also bring up a dialog asking you for number of smoothing points.
The smoothed curve will be in IFFT1_Real.
Note that the result from this script is slightly different from what the built-in tool does. This is because the tool internally pads the data to 2^n number of points and then does FFT etc. But this script could be a good starting point if you want to change/improve the filter.
One way to run this script is to edit custom.ogs file on your root Origin directory, then comment out lines below [Main] section, and paste this code under there. Then you can run code by clicking on the Custom Routine button on the Standard Toolbar.
In version 7, Origin is shipped with a selection of NAG numerical libraries, and also supports C programming - so filter code can be written using C and one can call NAG library for performing FFT etc.
Hope this helps you.
Easwar
OriginLab.
// First check if worksheets FFT1 and IFFT1 exist - if yes, clear them
if(exist(FFT1) == 2) clearworksheet FFT1;
if(exist(IFFT1) == 2) clearworksheet IFFT1;
// Perform forward FFT
fft.reset();
fft.forward = 1;
fft.forward.timeData$ = Data1_A;
fft.forward.tdelta = Data1_A[2] - Data1_A[1];
fft.forward.realData$ = Data1_B;
window -t W fft FFT1;
fft.output.samplingdata$ = FFT1_Freq;
fft.output.realdata$ = FFT1_Real;
fft.output.imagdata$ = FFT1_Imag;
fft.output.ampdata$ = FFT1_r;
fft.output.phasedata$ = FFT1_Phi;
fft.output.powerdata$ = FFT1_Power;
fft.real = 1;
fft.normalize = 0;
fft.shifted = 0;
fft.windowing = 1;
fft.spectrum = 1;
fft.unwrap = 0;
fft.forward();
// Bring up dialog and ask user for number of points for smoothing
getn "Enter number of smooth points;" nPts;
get Data1_A -e ii;
// Quit if number of points don't make sense
if( (nPts < 1) || (nPts > (ii/2)) )
{
type Num. of points incorrect!;
break;
}
// Compute cutoff frequency
FCutoff = 1 / ( nPts * (Data1_A[2] - Data1_A[1]) );
// Find index in FFT dataset where cutoff frequency occurs
ii1 = xindex(FCutoff, FFT1_Real);
// Find length of FFT dataset and find mirror point
get FFT1_Freq -e ii;
ii2 = ii - ii1;
// Create a Filter dataset
create Filter ii;
set Filter -e ii;
// Fill it first with all 1s
Filter = 1;
// Loop thru filter and create parabolic shape
loop(jj, 2, ii1)
{
Filter[jj] = sqrt(1 - jj^2/ii1^2);
Filter[ii-jj+2] = sqrt(1 - jj^2/ii1^2);
}
// Set middle values in filter to zero
loop (jj, ii1, ii2)
{
Filter[jj] = 0;
}
// Multiply FFT real and imaginary with Filter shape
FFT1_Real *= Filter;
FFT1_Imag *= Filter;
// Delete Filter dataset
delete Filter;
// Perform backward FFT
fft.reset();
fft.forward = 0;
fft.backward.freqData$ = FFT1_Freq;
fft.backward.fDelta = FFT1_Freq[2] - FFT1_Freq[1];
fft.backward.realData$ = FFT1_Real;
fft.backward.imagData$ = FFT1_Imag;
window -t W fft IFFT1;
fft.output.samplingdata$ = IFFT1_Freq;
fft.output.realdata$ = IFFT1_Real;
fft.output.imagdata$ = IFFT1_Imag;
fft.output.ampdata$ = IFFT1_r;
fft.output.phasedata$ = IFFT1_Phi;
fft.output.powerdata$ = IFFT1_Power;
fft.real = 1;
fft.normalize = 0;
fft.shifted = 0;
fft.windowing = 1;
fft.spectrum = 1;
fft.unwrap = 0;
fft.backward();
// End of script file
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| ubitelli@n1 |
Posted - 05/30/2003 : 2:06:24 PM
Any body here?
Nothing new on the FFT smoothing procedure?
What a hell of parabolic function!!!
I will try suicide.....
Ricardo. |
| ubitelli@n1 |
Posted - 05/22/2003 : 12:33:49 PM
Hi Easwar
I have made some calculations using your hints but
the things arenīt still good. Is the parabolic function
just a function of this type: 1-(1/Fc^2)*x^2 where Fc is
the cutoff frequency and x are the x axis values?
If this function is correct something is wrong with
my procedure.
What I am doing is taking the FFT of the y data, multiplying this
FFT by the function defined above and taking the inverse FFT.
The results donīt match with the Originīs results.
If you want I can send you the file with the data points.
I am using only 128 points.
Thanks
Ricardo.
PS.: I have Origin version 6.1
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| easwar |
Posted - 05/20/2003 : 4:56:52 PM
Hi Ricardo,
The cutoff frequency is determined using the formula:
FCutoff = 1 / (msmooth * xinc)
where msmooth is the number of smooth points you specify, and xinc is the increment/step value in time. xinc is computed as the difference between the first two x values.
A parabola is then generated that is symmetric about 0, and has a value of 1 at freq=0 and has a value of 0 at freq=FCutoff.
This parabola is used to filter/multiply the FFT spectrum, and the inverse FFT computation is performed to obtain the smoothed data.
If you are trying to code this yourself, and you want to play with the parabola/filter shape etc, I would recommend using the NAG fft functions - you can use the FFT() function under matrix.h - I am assuming here that you have version 7.
We will add this information to our documentation.
Easwar
OriginLab.
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| ubitelli@n1 |
Posted - 05/20/2003 : 1:56:06 PM
Hello Easwar
You are right. The cutoff canīt be so sharp.
Yes Easwar, I would like to know how this function is constructed.
Could you send me some information on this?
Thanks
Ricardo. |
| easwar |
Posted - 05/20/2003 : 1:17:55 PM
Hi Ricardo,
The cutoff is not a sharp cutoff, which would then be just a low pass filter. Rather it is a parabolic shape that falls off to zero at the cutoff frequency:
http://www.originlab.com/www/products/origin/analysis_fft_filter_smoothing.asp
Are you looking for more information, such as to how this parabola is constructed?
Easwar
OriginLab.
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