A spreadsheet, available in Excel
and in OpenOffice open document formats. 
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A simple demonstration script using the findpeaks
function on noisy synthetic data. Numbers the peaks and
prints out the P matrix in the Matlab command
window:
Peak # Position Height WidthDemoFindPeakSNR is a variant of DemoFindPeak.m that uses findpeaksnr.m to compute the signal-to-noise ratio (SNR) of each peak and returns it in the 5th column. |
[IdentifiedPeaks,AllPeaks]=idpeaks(DataMatrix,AmpT,SlopeT,sw,fw,maxerror,Positions,Names)It finds peaks in the signal "DataMatrix" (x-values in column 1 and y-values in column 2), according to the peak detection parameters AmpT, SlopeT, sw, fw (see the "findpeaks" function above), then compares the found peak positions (x-values) to a database of known peaks, in the form of an array of known peak maximum positions ('Positions') and matching cell array of names ('Names'). If the position of a peak found in the signal is closer to one of the known peaks by less than the specified maximun error ('maxerror'), that peak is considered a match and its peak position, name, error, and peak amplitude (height) are entered into the output cell array "IdentifiedPeaks". The full list of detected peaks, identified or not, is returned in "AllPeaks". Use "cell2mat" to access numeric elements of IdentifiedPeaks,e.g. cell2mat(IdentifiedPeaks(2,1)) returns the position of the first identified peak, cell2mat(IdentifiedPeaks(2,2)) returns its name, etc. Obviously for your own applications, it's up to you to provide your own array of known peak maximum positions ('Positions') and matching cell array of names ('Names') for your particular types of signals.
>> load DataTable
>> load spectrum
>> idpeaks(Cu,0.01,.001,5,5,.01,Positions,Names)
ans=
'Position' 'Name' 'Error' 'Amplitude'
[ 221.02] 'Cu II 221.027' [ -0.0025773] [ 0.019536]
[ 221.46] 'Cu I 221.458' [ -0.0014301] [ 0.4615]
[ 221.56] 'Cu I 221.565' [-0.00093125] [ 0.13191]
.................... etc...
  Press U key to switch
between peak and valley mode.
  Example 2   ECG data (normal and
inverted)
  Example 3
 Example 5. Pressing 'L'
toggles ON and OFF the peak labels in the upper window.
 Example 8. The peak
identification function applied to a high-resolution
atomic spectrum.
 Example 8. Three peaks near
296 nm isolated and identified. Press the I key to display
the peak ID names.
 Normal Peak Fit (N key)
 iPeak 3.2 and later, showing log scale (Y key) and Autozero mode (T key)  Click to view larger figures. |
iPeak is a keyboard-operated
Interactive Peak Finder for time series data, based on the "findpeaks.m" function,
for Matlab only. (What's
new in Version 5.3?) It accepts data in a single
vector, a pair of vectors, or a matrix with the
independent variable in the first column and the dependent
variable in the second column: Example 1: One input argument; data in single vector >> y=cos(.1:.1:100);ipeak(y) Example 2: One input argument; data in two columns of a matrix >> x=[0:.01:5]';y=x.*sin(x.^2).^2;M=[x y];ipeak(M) Example 3: Two input arguments; data in separate x and y vectors >> x=[0:.1:100];y=(x.*sin(x)).^2;ipeak(x,y); Example 4: Additional input argument (after the data) to control peak sensitivity. >> x=[0:.1:100];y=5+5.*cos(x)+randn(size(x));ipeak(x,y,10); or >> ipeak([x;y],10); or >> ipeak(humps(0:.01:2),3) or >> x=[0:.1:10];y=exp(-(x-5).^2);ipeak([x' y'],1) The additional numeric argument is an estimate of the ratio of the typical peak width to the length of the entire data record (PeakD). Small values detect fewer peaks; larger values detect more peaks. It effects only the starting values for the peak detection parameters. (This is just a quick way to set reasonable initial values of the peak detection parameters, rather than specifying each one individually as in the following example). iPeak displays the entire signal in the lower half of the Figure window and an adjustable zoomed-in section in the upper window. Pan and zoom the portion in the upper window using the cursor arrow keys. (Press Shift-C to change the plot color.) Adjust the peak detection parameters AmpThreshold (A/Z keys), SlopeThreshold (S/X), SmoothWidth (D/C), FitWidth (F/V) so that it detects the desired peaks and ignores those that are too small, too broad, or too narrow to be of interest. Detected peaks are numbered from left to right. Press P to display the peak table of all the detected peaks (Peak #, Position, Height, Width, Area). Press Shift-P to save peak table as disc file. Press U to switch between peak and valley mode (version 3.7 and above). Note: in version 5.1 and later, to speed up the operation for signals over 100,000 points in length, the lower window is refreshed only when the number of detected peaks changes or if the Enter key is pressed. Press K to see all the keystroke commands. Peak Summary Statistics. Version 5.3 (April, 2013) adds the E key command to print a table of summary statistics of the peak intervals (the x-axis interval between adjacent detected peaks), heights, widths, and areas, listing the maximum, minimum, average, and percent standard deviation, and displaying the histograms of the peak intervals, heights, widths, and areas in figure windows 2 through 5. Peak Summary Statistics 15 peaks detected Autozero OFF Interval Height Width Area Maximum 6.3795 10.5308 3.2354 34.943 Minimum 6.1649 9.7355 2.6671 29.9008 Mean 6.291 10.1559 3.0149 32.5771 % STD 0.91178 1.904 5.2584 4.3022 Example 5: Six input arguments. As above, but input arguments 3 to 6 directly specifies initial values of AmpThreshold (AmpT), SlopeThreshold (SlopeT), SmoothWidth (SmoothW), FitWidth (FitW) . PeakD is ignored in this case, so just type a '0' as the second argument after the data matrix). >> ipeak(datamatrix,0,.5,.0001,20,20); Keystrokes allow you to pan and zoom the upper window, to inspect each peak in detail if desired. You can set the initial values of pan and zoom in optional input arguments 7 ('xcenter') and 8 ('xrange'). See example 6 below. The peak cloest to the center of the upper window is labeled in the upper left of the top window, and it peak position, height, and width are listed. The Spacebar/Tab keys jump to the next/previous detected peak and displays it in the upper window at the current zoom setting (use the up and down cursor arrow keys to adjust the zoom range). The Y key toggles between linear and log y-axis scale in the lower window (a log axis is good for inspecting signals with high dynamic range; it effects only the lower window display and has no effect on the peak detection or measurements). Example 6: Eight input arguments. As above, but input arguments 7 and 8 specifiy the initial pan and zoom settings, 'xcenter' and 'xrange', respectively. In this example, the x-axis data are wavelengths in nanometers (nm), and the upper window zooms in on a very small 0.4 nm region centered on 249.7 nm. (These data, provided in the ZIP file, are from a high-resolution atomic spectrum). >> load ipeakdata.mat >> ipeak(Sample1,0,100,0.05,3,4,249.7,0.4); Autozero mode. The T key toggles the autozero mode off and on. When autozero is OFF, peak heights are measured relative to zero. (If the peaks are superimposed on a background, use the baseline subtract keys - B and G - first to subtract the background). When autozero is ON, peak heights are automatically measured relative to the local baseline on either side of the peak; use the zoom controls to isolate the peaks so that the signal returns to the local baseline between the peaks as displayed in the upper window. When autozero is ON, the peak heights, widths, and areas in the peak table (R or P keys) will be automatically corrected for the baseline. (Autozero OFF will give better results when the baseline is zero, or has been subtracted using the B key, even if the peaks are partly overlapped. Autozero ON will work best if the peaks are well separated so that the signal returns to the local baseline between the peaks. If the peaks are highly overlapped, or if they are not Gaussian in shape, the best results will be obtained by using the curve fitting function - the N or M keys). Example 7: Nine input arguments. As example 6, but the 9th input argument turns ON the autozero mode (equivalent to pressing the T key). If not specified, autozero is initially OFF. >> ipeak(Sample1,0,100,0.00,3,4,249.7,0.4,1); Normal and Multiple Peak fitting: The N key applies iterative curve fitting to the detected peaks that are displayed in the upper window (referred to here as "Normal" curve fitting). The use of the iterative least-squares function can result in more accurate peak parameter measurements that the normal peak table (R or P keys), especially if the peaks are non-Gaussian in shape or are highly overlapped. If the peaks are superimposed on a background, turn on the Autozero mode (T key). Then use the pan and zoom keys to select a peak or a group of overlapping peaks in the upper window, with the signal returning all the way to the local baseline at the ends of the upper window. Make sure that AmpThreshold, SlopeThreshold, SmoothWidth are adjusted so that each peak is numbered once. Then press the N key, type a number for the desired peak shape at the prompt in the Command window and press Enter (1=Gaussian (default), 2=Lorentzian, 3=logistic, 4=Pearson, 5=exponentially broadened Gaussian; 6=equal-width Gaussians; 7=Equal-width Lorentzians; 8=exponentially broadened equal-width Gaussian, 9=exponential pulse, 10=sigmoid, 11=Fixed-width Gaussian, 12=Fixed-width Lorentzian; 13=Gaussian/Lorentzian blend; 14=bifurcated Gaussian, 15=bifurcated Lorentzian), then type in a number of repeat trial fits and press Enter (the default is 1; start with that and then increase if necessary). If you have selected a variable-shape peak (numbers 4, 5, 8 ,13, 14, or 15), the program will ask you to type in a number that controls the shape ("extra" in the peakfit input arguments). The program will then perform the fit, display the results graphically in Figure window 2, and print out a table of results in the command window, e.g.: Peak shape (1-8): 2 Number of trials: 1 Least-squares fit to Lorentzian peak model Fitting Error 1.1581e-006% Peak# Position Height Width Area 1 100 1 50 71.652 2 350 1 100 146.13 3 700 1 200 267.77 There is also a "Multiple" peak fit function (M key) that will attempt to apply iterative curve fitting to all the detected peaks in the signal simultaneously. Before using this function, it's best to turn off the Autozero (T key) and use the multi-segment baseline correction function (B key) to remove the background (because the autozero function will probably not be able to subtract the baseline from the entire signal). Then press M and proceed as for the normal curve fit. A multiple curve fit may take a minute or so to complete if the number of peaks is large, possibly longer than the Normal curve fitting function on each group of peaks separately. Make sure all the peaks are detected and numbered before activating this function, because it depends on the peak table for the number of peaks and the starting values, and it will fit only those peaks that it has already located and numbered. The N and M key fitting functions perform non-linear iterative curve fitting using the peakfit.m function. The number of peaks and the starting values of peak positions and widths for the curve fit function are automatically supplied by the the findpeaks function, so it is essential that the peak detection variables in iPeak be adjust so that all the peaks in the selected region are detected and numbered once. (For more flexible curve fitting, use ipf.m, which allows manual optimization of peak groupings and start positions). Note 1: If the peaks are too overlapped to be detected and numbered separately, try pressing the H key to activate the sharpen function before pressing M (version 4.0 and above only). Note 2: If you plan to use a variable-shape peak (numbers 4, 5, 8 ,13, 14, or 15) for the Multiple peak fit, it's a good idea to obtain a reasonable value for the requested "extra" shape parameter by performing a Normal peak fit on an isolated single peak (or small group of partly-overlapping peaks) of the same shape, then use that value for the Multiple curve fit of the entire signal. Note 3: Although the peak widths can vary from peak to peak, the curve fit routines assume that the peak shape is the same for all peaks in one fitting operation, so if the peak shape varies accross the signal, use the Normal peak fit to fit each section with a different shape rather than the Multiple peak fit. Peak identification. There is an optional "peak identification" function if optional input arguments 9 ('MaxError'), 10 ('Positions'), and 11 ('Names') are included. The "I" key toggles this function ON and OFF. This function compares the found peak positions (maximum x-values) to a database of known peaks, in the form of an array of known peak maximum positions ('Positions') and matching cell array of names ('Names'). If the position of a found peak in the signal is closer to one of the known peaks by less than the specified maximun error ('MaxError'), then that peak is considered a match and its name is displayed next to the peak in the upper window. When when the 'O' key is pressed (the letter 'O'), the peak positions, names, errors, and amplitudes are printed out in a table in the command window. Example 8: Eleven input arguments. As above, but also specifies 'MaxError', 'Positions', and 'Names' in optional input arguments 9, 10, and 11, for peak identification function. Pressing the 'I' key toggles off and on the peak identification labels in the upper window.These data (provided in the ZIP file) are from a high-resolution atomic spectrum (x-axis in nanometers). >> load ipeakdata.mat >> ipeak(Sample1,0,100,0.05,3,6,296,5,0.1,Positions,Names); Pressing "O" prints the peak positions, names, errors, and amplitudes in a table in the command window. Name Position Error Amplitude 'Mg I 295.2' [295.2] [0.058545] [129.27] 'Cu 296.1 nm' [296.1] [0.045368] [124.6] 'Hg 297.6 nm' [297.6] [0.023142] [143.95] Note: The ZIP file contains the latest version of the iPeak function as well as some sample data to demonstrate peak identification (Example 8). Obviously for your own applications, it's up to you to provide your own array of known peak maximum positions ('Positions') and matching cell array of names ('Names') for your particular types of signals. Keyboard Controls: Pan signal left and right...Coarse pan: < or > Fine pan: left or right cursor arrow keys Nudge one point left or right: [ and ] Zoom in and out.............Coarse zoom: / or ' Fine zoom: up or down cursor arrow keys Resets pan and zoom.........ESC Refresh entire plot.........Enter (Updates cursor position in lower plot) Change plot color...........Shift-C (cycles through standard colors) Adjust AmpThreshold.........A,Z (Larger values ignore short peaks) Adjust SlopeThreshold.......S,X (Larger values ignore broad peaks) Adjust SmoothWidth..........D,C (Larger values ignore sharp peaks} Adjust FitWidth.............F,V (Adjust to cover just top part of peaks) Toggle sharpen mode ........H Helps detect overlapped peaks. Baseline correction.........B, then click baseline at multiple points Restore original signal.....G to cancel previous background subtraction Invert signal...............- Invert (negate) the signal (flip + and -) Set minimum to zero.........0 (Zero) Sets minimum signal to zero Toggle log y mode OFF/ON....Y Plot log Y axis on lower graph Toggle autozero OFF/ON......T Auto background subtraction on upper graph Toggle valley mode OFF/ON...U Switch to valley mode Print peak table............P Prints Peak #, Position, Height, Width Save peak table.............Shift-P Saves peak table as disc file Step through peaks..........Space/Tab Jumps to next/previous peak Normal peak fit.............N Fit peaks in upper window with peakfit.m Multiple peak fit...........M Fit all peaks in signal with peakfit.m Print keyboard commands.....K Prints this list Print findpeaks arguments...Q Prints findpeaks function with arguments. Print ipeak arguments.......W Prints ipeak function with all arguments. Print report................R Prints Peak table and parameters Print peak statistics.......E prints mean, std of peak intervals, heights, etc. Peak labels ON/OFF......... L Label all peaks detected in upper window. Peak ID ON/OFF..............I Identifies closest peaks in 'Names' database. Print peak IDs..............O Prints table of peaks IDs *Sunspot data downloaded from NOAA: ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/yearly/YEARLY.PLT |
demoipeak.m is a simple demo script that generates a noisy signal with peaks, calls iPeak, and then prints out a table of the actual peak parameters and a list of the peaks detected and measured by iPeak for comparison. Before running this demo, ipeak.m must be downloaded and placed in the Matlab path. The ZIP file at http://terpconnect.umd.edu/~toh/spectrum/ipeak5.zip contains several demo scripts (ipeakdemo.m, ipeakdemo1.m, etc) that illustrate various aspects of the iPeak function and how it can be used effectively. Download the zip file, right-click and select "Extract all", then put the resulting files in the Matlab path and run them by typing their names at the Matlab command window prompt or by opening them in the Matlab editor and clicking the green "Run" button on the editor toolbar. To test for the proper installation and operation of iPeak, you can run this test script.
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ipeakdemo: effect of
the peak detection parameters Four Gaussian peaks with the same heights but different widths (10, 30, 50 and 70 units) This demonstrates the effect of SlopeThreshold and SmoothWidth on peak detection. Increasing SlopeThreshold (S key) will discriminate against the broader peaks. Increasing SmoothWidth (D key) will discriminate against the narrower peaks and noise. FitWidth (F/V keys) controls the number of points around the "top part" of the (unsmoothed) peak that are taken to estimate the peak heights, positions, and widths. A reasonable value is ordinarily about equal to 1/2 of the number of data points in the half-width of the peaks. In this case, where the peak widths are quite different, set it to about 1/2 of the number of data points in the narrowest peak. |
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ipeakdemo1: the autozero mode Demonstration of autozero background correction, for separated, narrow peaks on a large baseline. Each time you run this demo, you will get a different set of peaks and noise. A table of the actual peak positions, heights, widths, and areas is printed out in the command window. Jump to the next/previous peaks using the Spacebar/Tab keys. Hint: Turn on the Autozero mode (T key), adjust the zoom setting so that the peaks are shown one at a time in the upper window, then press the P key to display the peak table. |
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ipeakdemo2: peak
overlap and the curve fitting functions.
Demonstration of error caused
by overlapping peaks on a large offset baseline. Each time you run this demo, you will get a
different set of peaks and noise. A table of the actual peak positions, heights,
widths, and areas is printed out in the command
window. Jump to the
next/previous peaks using the Spacebar/Tab
keys. Hint: Use the B key and click on the baseline points, then press the P key to display the peak table. Or turn on the Autozero mode (T key) and use the Normal curve fit (N key) or Multiple curve fit (M key) with peak shape 1 (Gaussian). |
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ipeakdemo3: Non-Gaussian peak shapes Demonstration of overlapping
Lorentzian peaks, without an added background. Overlap
of peaks causes significant errors in peak height,
width, and area. Jump to the
next/previous peaks using the Spacebar/Tab
keys. Each time you run
this demo, you will get a different set of noise. A table of the actual peak positions, heights,
widths, and areas is printed out in the command
window. Hint: turn OFF the Autozero mode (T key) and use the Normal curve fit (N key) or Multiple curve fit (M key) with peak shape 2 (Lorentzian). |
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ipeakdemo4: dealing
with very noisy signals Detection and measurement of
four peaks in a very noisy signal. The signal-to-noise
ratio of first peak is 2. Each time you run this demo, you will get a
different set of noise. A table of the actual peak positions, heights,
widths, and areas is printed out in the command
window. Jump to the
next/previous peaks using the Spacebar/Tab
keys. The peak at x=100
is usually detected, but the accuracy of peak
parameter measurement is poor because of the low
signal-to-noise ratio. Hint: With very noisy signals it is usually best to increase SmoothWidth and FitWidth to help reduce the effect of the noise. |
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ipeakdemo5: dealing
with highly overlapped peaks In this demo the peaks are so
highly overlapped that only one or two of the highest
peaks yield distinct maxima that are detected by
iPeak. The height, width, and area estimates are
highly inaccurate because of this overlap. The normal
peak fit function ('N'
key) would be useful in this case, but it depends on
iPeak for the number of peaks and for the initial
guesses, and so it would fit only the peaks that were
found and numbered. To help in this case, pressing the 'H' key will activate the peak sharpen function that decreases peak width and increases peak height of all the peaks, making it easier to detect and number all the peaks for use by the peakfit function (N key). Note: peakfit fits the original unmodified peaks; the sharpening is used only to help locate the peaks to provide peakfit with suitable starting values.. |
Which to use: iPeak or Peakfit? Download these Matlab demos that compare iPeak.m with Peakfit.m for signals with a few peaks and signals with many peaks and that shows how to adjust iPeak to detect broad or narrow peaks. These are self-contained demos that include all required Matlab functions. Just place them in your path and click Run or type their name at the command prompt. Or you can download all these demos together in idemos.zip.
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Interactive findpeaks script using mouse-controlled
sliders for interactive control. Requires Matlab 6.5. This
can be used to determine what values of the parameters give
the most reliable peak detection. Load your data set into
the vectors x and y (x = independent variable, y = dependent
variable), then run this m-file and adjust the sliders to
change the four arguments of the peakfind function. The four
sliders correspond to the arguments of the findpeaks
function described above: SlopeThreshold (SlopeT), AmpThreshold
(AmpT), SmoothWidth (Smooth), and FitWidth
(Fit). The range of these sliders is easily changed in
lines 65 - 70 to suit a wide range of data types. The BG
button is used for baseline (background) subtraction: click
once on the BG button, then click on the baseline at
five points starting to the left of the lowest x-value and
ending to the right of the highest x-value. The background
will be subtracted. You can repeat as needed. (You can also
change the number of baseline points by changing
BaselinePoints in the function BG.m). Peak number and the
estimated position, height, and width of each peak is
returned in the matrix P:
>> P |
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A self-contained interactive demonstration of FindPeakSliders applied to noisy synthetic data set consisting of a random number of narrow peaks superimposed on a gently curved background. Requires Matlab 6.5. Use the sliders to explore the effect of the variables SlopeThreshold (SlopeT), AmpThreshold (AmpT), SmoothWidth (Smooth), and FitWidth (Fit), and the baseline correct (BG) button. Peak number and the estimated position, height, and width of each peak is returned in the matrix P. |
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A self-contained interactive demonstration of
FindPeakSliders applied to a data set containing four simple
peaks with increasing peak height and peak width. Use this
to understand the difference between the variables
SlopeThreshold (SlopeT), which discriminates on the basis of
peak width, and AmpThreshold (AmpT), which discriminates on
the basis of peak amplitude. Peak number and the estimated
position, height, and width of each peak is returned in the
matrix P.
>> P |
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The spreadsheet pictured above implements the "findpeaks" peak finding and measurement method in a spreadsheet. The input x,y data are contained in Sheet1, column A and B, rows 8 to 263. You can Copy and Paste your own data there. The amplitude threshold and slope threshold are set in cells B3 and E3, respectively.
Smoothing and differentiation are performed by the convolution technique used by the spreadsheets DerivativeSmoothing.xls described previously. The Smooth Width and the Fit Width are both controlled by the number of non-zero convolution coefficients in row 5, columns J through Z. (In order to compute a symmetrical first derivative, the coefficients in columns J to Q must be the negatives of the positive coefficients in columns S to Z). The original data and the smoothed derivative are shown in the two charts on Sheet1.
To detect peaks in the data, a series of three conditions
are tested for each data point in columns F, G, and H,
corresponding to the three nested loops in findpeaks.m:
If the answer to all three questions is yes (highlighted by blue cell coloring), a peak is registered at that point (column I), counted in column J, and assigned an index number in column K.
For the first 10 peaks found, the x,y original unsmoothed data are copied to Sheets 2 through 11, respectively, where that segment of data is subjected to a Gaussian least-squares fit, using the same technique as GaussianLeastSquares.xls. The best-fit Gaussian parameter results are copied back to Sheet1, in the table in columns AH-AK. (In its present form. the spreadsheet is limited to measuring 10 peaks, although it can detect any number of peaks. Also it is limited in Smooth Width and Fit Width by the 17-point convolution coefficients).
The spreadsheet is available in OpenOffice (ods) and in Excel (xls) and (xlsx) formats. They are functionally equivalent and differ only in minor cosmetic aspects. An example spreadsheet, with data, is available. A demo version, with a calculated noisy waveform that you can modify, is also available.
A comparison of this spreadsheet to its Matlab/Octave equivalent findpeaksplot.m is instructive. On the positive side, the spreadsheet literally "spreads out" the data and the calculations spatially over a large number of cells and sheets, breaking down the discrete steps in a very graphic way. In particular, the use of conditional formatting in columns F through K make the peak detection decision process more evident for each peak, and the least-squares sheets 2 through 11 lay out every detail of those calculations. Spreadsheet programs have many flexible and easy-to-use formatting options to make displays more attractive. On the down side, a spreadsheet as complicated as this one is far more difficult to construct than its Matlab/Octave equivalent. Much more serious, the spreadsheet is less flexible and harder to expand to larger signals and larger number of peaks. In contrast, the Matlab/Octave equivalent, while requiring some understanding of programming, is faster, much more flexible, and can easily handle signals and smooth/fit widths of any size. Moreover, because it is written as a Matlab/Octave function, it can be readily employed as an element in your own custom Matlab/Octave programs to perform even larger tasks.
Tom O'Haver
Professor Emeritus
Department of Chemistry and Biochemistry
The University of Maryland at College Park
toh@umd.edu
http://terpconnect.umd.edu/~toh/
Last updated, May, 2013
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