Convolution using the FFT
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The convolution of two data sets is a general process that
can be used for various types of data smoothing, signal processing,
or edge detection. It's main purpose is to include the effect
of system response on a signal.
Convolution in Origin...
In order to perform a convolution in Origin, the leftmost
data set in your worksheet selection should represent the
signal data set and the response data set should
be placed immediately to its right. The response data set
should meet the following requirements:
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Click on the image to see a full example
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- The response data set should consist of an odd number of points
and be a representative sample of a symmetric function.
- The number of points in the response data set must be less
than half the number of points in the signal data set.
- The sum of the points in the response curve should be unity
in order to retain the amplitude of the original data set. Otherwise
the convolution result will be scaled by a factor equal to the
sum.
To avoid possible artifacts from the FFT (performed as part of
the convolution process), the signal data must be padded with zero
values until the number of points is equal to an integral power
of two. The X data must be extended accordingly.
Once the data is set up properly, the convolution is performed
by highlighting both data sets (the signal and response) and selecting
the Analysis:Convolute menu. Origin adds two columns to the
rightmost position in the worksheet. The left column holds the index
variables, and the right column holds the convolution result.
View
an example...
Other options...
Origin - Data Analysis -
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