Video Demonstration
The "enhance" command-line function
function Enhancedsignal=enhance(signal,factor1,factor2,SmoothWidth)
Basic function for resolution enhancement by the even-derivative
method. The arguments factor1 and factor2 are the weighting factors
for the 2^{nd} and 4^{th} derivatives.
SmoothWidth is the width of the
smoothing function applied to the derivatives. Optimum values for
factor1 and factor2 depend
on the width and the shape of the peaks in the signal, and
also on the desired trade-off between resolution enhancement
(peak width reduction) and baseline artifacts that are a
by-product of the method. As a starting point, a reasonable
value for factor1 is PeakWidth^{2}/25 and for factor 2
is PeakWidth^{4}/833 for peaks of Gaussian shape
(or PeakWidth^{2}/6 and PeakWidth^{4}/700
for Lorentzian peaks), where PeakWidth is the full-width at half
maximum of the peaks expressed in number of data points. The easiest
way to determine the optimum values for your data is to use iSignal or
InteractiveResEnhance, described below.
Interactive Resolution Enhancement using the iSignal function
iSignal is
a Matlab function that performs resolution enhancement for time-series
signals, using the above enhance function, with keystrokes that allow
you to adjust the 2^{nd} and 4^{th} derivative weighting factors and the smoothing continuously while observing the effect on your signal dynamically. View the code here or dowload the ZIP file with sample data for testing. Just place isignal.m in the Matlab path and type
>> isignal(DataMatrix); or
>> isignal(x,y); or
>> isignal(y);
where DataMatrix is a matrix with x values in the first row or column and y values in the second. Press K to see all the keyboard commands. Use the cursor arrow keys to pan and zoom.
The E key turns the resolution enhancement function on and off. iSignal is
particularly convenient to use because it calculates the sharpening and
smoothing settings for Gaussian and for Lorentzian peak shapes using the Y and U keys, respectively. Just isolate a single typical peak in the upper window using the pan and zoom keys, then press Y for Gaussian or U for Lorentzian peaks. (The
optimum settings depends on the width of the peak, so if your signal
has peaks of widely different widths, one setting will not be optimum
for all the peaks). You can fine-tune the sharpening with the F/V and G/B keys and the smoothing with the A/Z keys. Press K to see all the keyboard commands.
The graphic example on the right is the result of the following commands:
>> x=[0:.005:2];y=humps(x);Data=[x;y];
>> isignal(Data,0.3,0.5,1,3,1,0,1,220,5400);
Press the 'E' key to toggle sharpening ON/OFF to compare before and after peak sharpening.
Interactive optimization of derivative resolution enhancement for your own data. Requires Matlab 6.5. To use this, place the data to be enhanced in the global vector "signal", then execute this file. It plots the data and displays sliders for separate real-time control of 2^{nd} and 4^{th} derivative weighting factors (factor and factor2) and smooth width. (Larger values of factor1 and factor2 will reduce the peak widths but will cause artifacts in the baseline near the peak. Adjust the factors for the best trade-off). Use the minimum smooth width needed to reduce excess noise. The resolution-enhanced signal is placed in the global vector "Enhancedsignal". (If the range of the sliders is inappropriate for your signal, you can adjust the slider ranges in lines 27-29). |
Self-contained demo of resolution enhancement for a simulated signal of four overlapping peaks. Requires Matlab 6.5. Displays sliders for separate real-time control of 2^{nd} and 4^{th} derivative weighting factors (factor and factor2) and smooth width. Larger values of factor1 and factor2 will reduce the peak width but will also cause artifacts in the baseline near the peak. Adjust these factors for the the best compromise. Use the minimum smooth width needed to reduce excess noise (too much smoothing will reduce the resolution enhancement). |
Similar to DemoResEnhance, but for a single Gaussian peak. This allows you to experiment with the adjustable parameters that work best for a peak of Gaussian shape. You can change the width of the peak in line 26. The estimated width of the resolution-enhanced peak is computed and displayed above the graph, to make it easier to determine the extent of resolution enhancement quantitatively. Try to adjust the parameters until the estimated peak width is as small as possible, while still giving acceptable baseline flatness. |
Similar to DemoResEnhance, but for a single Lorentzian peak. Requires Matlab 6.5. This allows you to experiment with the adjustable parameters that work best for a peak of Lorentzian shape. You can change the width of the peak in line 26. The estimated width of the resolution-enhanced peak is computed and displayed above the graph, to make it easier to determine the extent of resolution enhancement quantitatively. Try to adjust the parameters until the estimated peak width is as small as possible, while still giving acceptable baseline flatness. |
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