Y=isignal(Data);
or Y=isignal(Data,xcenter,xrange,SmoothMode,SmoothWidth,ends,DerivativeMode,Sharpen,Sharp1,Sharp2,SlewRate,MedianWidth);
"Data"
may be a 2-column matrix with the
independent variable (x-values) in the first column and dependent
variable (y values) in the second column, or separate x and y
vectors, or a single y-vector (in which case the data points are
plotted against their index numbers on the x axis). Only the first
argument (Data) is required; all the others are
optional. Returns the processed independent axis (Y) vector as the
output argument. Plots the data in the figure window, the lower half of
the window showing the entire signal, and the upper half showing a
selected portion controlled by the pan and zoom keystrokes, with the
initial pan and zoom settings optionally controlled by input arguments 'xcenter' and 'xrange',
respectively. Other keystrokes allow you to control the smooth type,
width, and ends treatment, the derivative order (0th through 5th), and
peak sharpening. (The initial values of all these parameters can be
passed to the function via the optional input arguments SmoothMode, SmoothWidth, ends, DerivativeMode, Sharpen, Sharp1, Sharp2, SlewRate, and MedianWidth. See the examples below). Press K to see all the keyboard commands.
Smoothing
Reference: http://terpconnect.umd.edu/~toh/spectrum/Smoothing.html The S key (or input argument "SmoothMode") cycles through five smoothing modes: If SmoothMode=0, the signal is not smoothed. If SmoothMode=1, rectangular (sliding-average or boxcar) If SmoothMode=2, triangular (2 passes of sliding-average) If SmoothMode=3, pseudo-Gaussian (3 passes of sliding-average)
If SmoothMode=4, Savitzky-Golay smooth (thanks to Diederick). The A and Z keys (or optional input argument SmoothWidth) control the SmoothWidth, w. Example shown in the figure on the right. The X key toggles "ends" between 0 and 1. This determins how the "ends" of the signal (the first w/2 points and the last w/2 points) are handled when smoothing: If ends=0, the ends are zero. If ends=1, the ends are smoothed with progressively smaller smooths the closer to the end.
Generally, ends=1 is best, except in some cases using the derivative mode when ends=0 result in better vertical centering of the signal. Note:
when you are smoothing peaks, you can easily measure the effect of smoothing on
peak height and width by turning on peak measure mode (press P) and then press S to cycle through the smooth modes.
In
version
2.1
and above there are two special functions for removing or reducing sharp spikes
in signals: the M
key, which implements a median filter (it asks you to enter the spike
width, e.g. 1,2, 3... points) and the ~
key, which limits the maximum rate of change.
Differentiation
Reference: http://terpconnect.umd.edu/~toh/spectrum/Differentiation.html The
D
/ Shift-D
keys (or optional input argument “DerivativeMode”)
increase/decrease the derivative order. The default is 0. Careful
optimization of smoothing of derivatives is critical for acceptable
signal-to-noise ratio. Example shown in the figure on the right. In
iSignal version 1.9 and above, in SmoothModes 1 through 3, derivatives are computed with respect to the
independent variable (x-values), corrected for non-uniform x axis
intervals. In SmoothMode 4 (Savitzky-Golay) the derivatives are computed by the Savitzky-Golay algorithm.
Peak sharpening (resolution enhancement) Reference: http://terpconnect.umd.edu/~toh/spectrum/ResolutionEnhancement.html The E key (or optional input argument "Sharpen") turns off and on peak sharpening (resolution enhancement). The sharpening strength is controled by the F and V keys (or optional input argument "Sharp1") and B and G keys (or optional argument "Sharp2"). The optimum values depend on the peak shape and width. For peaks of Gaussian shape, a reasonable value for Sharp1 is PeakWidth2/25 and for Sharp2 is PeakWidth4/800 (or PeakWidth2/6 and PeakWidth4/700 for Lorentzian peaks), where PeakWidth is the full-width at half maximum of the peaks expressed in number of data points.
However, you don't need to do the math yourself; iSignal can calculate 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 Yfor 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. You can expect a decrease in peak width (and corresponding increase in
peak height) of about 20% - 50%, depending on the shape of the peak (the peak area is largely uneffected by sharpening).
Excessive sharpening leads to baseline artifacts and increased noise. iSignal
allows you to experimentally determine the values of these parameters
that give the best trade-off between sharpening, noise, and baseline
artifacts, for your purposes. You can easily measure the effect of
sharpening quantitatively by turning on peak measure mode (press P) and then press E to toggle the sharpen mode off and on. Note:
In
iSignal version 1.9 and above, only the Savitzky-Golay smooth mode is
used for peak sharpening. Example shown in the figure on the right.
Signal measurement
The cursor keys control the position of the green cursor (left and right arrow keys) and the distance between the dotted
red cursors (up and down arrow keys) that mark the selected range displayed in the upper graph
window. The label under the top graph window shows the value of the
signal (y) at the green cursor, the peak-to-peak (min and max) signal
range, the area under the signal, and the standard deviation within the
selected range (the dotted cursors). Pressing
the Q key prints out a table of the signal information in the command window.
Signal is measured by placing the
green center cursor on top of the peak
Noise is the standard deviation measured on a flat portion of the baseline
Signal-to-noise ratio (SNR) measurement of a signal with very
high SNR. Left:
The peak height of the largest signal peak is measured by placing the
green center cursor on the largest peak; peak-to-peak signal=66,000.
Right: The noise is measured on a flat portion of the baseline:
standard deviation of noise=0.01, therefore the SNR=66,000/.01 =
6,600,000
Version 2.8 adds a Frequency Spectrum mode toggled on and off by the Shift-S
key, which computes the Fourier frequency spectrum of the segment
of the signal displayed in the upper window and displays it in the
lower window (temporarily replacing the full-signal display). Use the
pan and zoom keys to adjust the region of the signal to be viewed. Press Shift-A to cycle through four plot modes (linear, semilog X, semilog Y, or log-log) and press Shift-X to toggle between a frequency on the x axis and time on the x-axis. The frequency (or time) and the harmonic number of the largest
component of the spectrum is displayed on the left. All signal
processing functions remain active in the frequency spectrum mode
(smooth, derivative, etc) so you can observe the effect of these
functions on the frequency spectrum of the signal. Press Shift-S again to return ro the normal mode. Example on the right.
Background subtraction There are two ways to subtract the background from the signal. Pressing the T
key toggles off and on the autozero mode. When Autozero is ON, the
program automatically
subtracts a
baseline from the segment of signal displayed in the upper window. The
baseline is
calculated by computing a quadratic least-squares fit to the signal in
the first 1/10th of the
points and the signal last 1/10th of the points. Try to
adjust the pan and
zoom to include some of the baseline at the beginning and end of the
segment in
the upper window, allowing the automatic baseline subtract gets a good
reading of the baseline. The calculation of the signal amplitude,
peak-to-peak signal, and peak area are all recalculated based on
the baseline-subtracted signal in the upper window. If you are
measuring peaks superimposed on a background, the use of the autozero
mode will have a big effect on the measured peak height, width,
and area, but very little effect on the peak x-axis position, as
demonstrated by these two figures.
In
addition to the autozero basline subtraction mode for peak measurement,
a background (or baseline) can be subtracted manually from the entire signal in one operation. The Backspace
key starts
background correction operation. In the command window, type in the
number of background points to click and press the Enter key. The
cursor changes to crosshairs;
click along the presumed background in the figure window, starting to the left of the x axis
and placing the last click to the right of the x axis. When the
last
point is clicked, the linearily interpolated baseline between those
points is subtracted from the signal. To restore the original
background (i.e. to start over), press the '\' key (just below the backspace key).
Peak and valley measurement
The P
key toggles off and on
the "peak parabola" mode, which attempts to measure the one peak (or
valley) that is centered in the upper
window under the green cursor by superimposing a least-squares
best-fit parabola, in red, on the center portion of the signal
displayed in the upper window. (Zoom in so
that the red overlays just the top of the peak or the bottom of the
valley as closely as possible). The
peak position, height, and "Gaussian width" are measured by
least-squares curve
fitting of a parabola to the isolated peak. The "RSquared" value is the
coefficient of determination; the closer to 1.000 the better. The
peak widths will most accurate if the peaks are Gaussian; other shapes,
and very noisy peaks of any shape, will give only approximate results.
However, the position, height, and area values are
pretty good for any peak shape as long as the "RSquared" value is at
least 0.99. The "total area" is measured
by the trapezoidal method over the entire selected segment displayed in
the
upper window. The "SNR" is the signal-to-noise-ratio of the peak under
the green cursor; it's the ratio of the peak height to the standard
deviation of the residuals between the data and the best-fit line in
red (version 2.4 and above). Example shown in the figure on the right. If the peaks are superimposed on
a non-zero background, subtract the background before measuring peaks,
either by using the autozero mode (T key) or the multi-point background
subtraction (backspace key). Press the R key to print out the peak parameters in the command window.
In version
2.2 and above, peak area is measured two ways: the "Gaussian area" and the "Total
area". The "Gaussian area" is the area under the Gaussian that
is best fit to the center portion of the signal
displayed in the upper window, marked in red. The "Total area" is
the area by the trapezoidal method over the entire selected segment
displayed in
the
upper window. If the portion of the signal displayed in the upper
window is a pure Gaussian with no noise and a zero baseline, then the
two measures should agree almost exactly. If the peak is not
Gaussian in shape, then the total area is likely to be more accurate,
as long as the peak is well separated from other peaks.
Version 2.6 adds an iterative curve fitting method performed by peakfit.m. This is the
most accurate method for the measurements of the areas of highly
overlapped peaks. Press the Shift-F
key, then select the desired peak shape from the menu, enter the number
of peaks and the number of repeat trial fits. A graph of the fit
is displayed in Figure window 2 and a table of results is printed out
in the command window. Note: for more flexible curve fitting, use ipf.m, which allows manual optimization of peak groupings and start positions. See Peak Fitter for details.
Saving the results
To save the processed signal to the disc as a x.y matrix in a.mat file,
press the 'o' key, the type in the desired file name, then press Enter
or click Save.
Other keystroke controls
The L
key toggles off and on
the Overlay mode, which shows the original signal as a dotted line
overlayed on the current processed signal, for the purposes of
comparison. The tab key restores the original signal and cursor settings. The ";"
key sets the selected region to zero (to eliminate artifacts and
spikes). The "-" (minus sign) key is used to negate the signal (flip +
for -). Press H
to toggle display of semilog y plot in the lower window, which is useful for
signals with very wide dynamic range, as in the example in the figures below (zero and negative points are
ignored in the log plot).
Linear y-axis mode
Log y mode (H key)
The C key condenses the signal by the specified factor n, replacing each group of n points with their average (n must be an integer, such as 2,3, 4, etc). The I key replaces the signal with a linearily interploated version containing m
data points. This can be used either to increase or decrease the x-axis
interval of the signal or to convert unevenly spaced values to evenly
spaced values. After pressing C or I, you must type in the value of n or m respectively.
Press K to see all the keyboard commands.
EXAMPLE 1: Single input argument; data in a two columns of a matrix [x;y] or in a single y vector >> isignal(y); >> isignal([x;y]);
EXAMPLE 2: Two input arguments. Data in separate x and y vectors. >> isignal(x,y);
EXAMPLE 3: Three or four input
arguments. The last two arguments specify the initial values of pan
(xcenter) and
zoom (xrange) in the last two input arguments. Using data in the ZIP
file:
>> load data.mat >> isignal(DataMatrix,180,40); or >> isignal(x,y,180,40);
EXAMPLE 4: As above, but
additionally specifies initial values of SmoothMode, SmoothWidth, ends,
and DerivativeMode in the last four input arguments. >> isignal(DataMatrix,180,40,2,9,0,1); EXAMPLE 5: As above, but
additionally specifies initial values of the peak sharpening parameters
Sharpen, Sharp1, and Sharp2 in the last three input arguments. Press the E key to toggle sharpening on and off for comparison.
>> isignal(DataMatrix,180,40,4,19,0,0,1,51,6000);
EXAMPLE 6: Using the built-in "humps" function:
>> x=[0:.005:2];y=humps(x);Data=[x;y];
4th derivative of the peak at x=0.9: >> isignal(Data,0.9,0.5,1,3,1,4); (shown on the right)
Peak sharpening applied to the peak at x=0.3:
>> isignal(Data,0.3,0.5,1,3,1,0,1,220,5400); (shown on the right)
(Press 'E' key to toggle sharpening ON/OFF to compare)
EXAMPLE 7:
Measurement of peak area. This example generates four Gaussian
peaks, all with the exact same peak height (1.00) and area (1.77). The
first peak (at x=4) is isolated, the second peak (x=9) is slightly
overlapped with the third one, and the last two peaks (at x= 13 and 15)
are strongly overlapped. To measure the area under a peak using
the perpendicular drop method, position the dotted red marker lines at
the minimum between the overlapped peaks.
Greater accuracy in peak area measurement using iSignal can be obtained by using the peak sharpening function to
reduce the overlap between the peaks. This reduces the peak widths,
increases the peak heights, but has no effect on the peak areas.
EXAMPLE 8:
Single peak with random spikes (shown in the figure on the right). Compare smoothing vs spike filter (M
key) and slew rate limit (~
key) to remove spikes.
KEYBOARD CONTROLS (Version 2.71): Pan left and right..........Coarse pan: < and >
Fine pan: left and right cursor arrows
Nudge: [ and ] Zoom in and out.............Coarse zoom: / and "
Fine zoom: up and down cursor arrows Resets pan and zoom.........ESC Adjust smooth width.........A,Z (A=>more, Z=>less)
Adjust smooth type..........S (None, Rectanglular, Triangle, Gaussian, Savitzky-Golay) Toggle smooth ends..........X (0=ends zeroed 1=ends smoothed (slower) Adjust derivative order.....D/Shift-D Increase/Decrease derivative order Toggle peak sharpening......E (0=OFF 1=ON) Sharpening for Gaussian.....Y Set sharpen settings for Gaussian Sharpening for Lorentzian...U Set sharpen settings for Lorentzian Adjust sharp1...............F,V F=>sharper, V=>less sharpening Adjust sharp2 ............G,B G=>sharper, B=>less sharpening Slew rate limit (0=OFF).....~ Largest allowed y change between points Spike filter width (0=OFF)..Mmedian filter eliminates sharp spikes (New) Toggle peak parabola........P fits parabola to center, labels vertex Fits peak in upper window...Shift-F (Asks for shape, number of peaks, etc) Spectrum mode on/off........Shift-S (Shift-A and Shift-X to change axes) Print peak report...........R prints position, height, width, area Toggle overlay mode.........L Overlays original signal as dotted line Toggle log y mode...........H semilog plot in lower window Toggle Autozero OFF/ON......T Subtracts background from upper window segment Restores original signal....Tab key resets to original signal and modes Baseline subtraction........Backspace, then click baseline at multiple points Restore background..........\ to cancel previous background subtraction Invert signal...............- Invert (negate) the signal (flip + and -) Remove offset...............0 (zero) set minimun signal to zero Sets region to zero.........; sets selected region to zero. Condense signal.............C Condense oversampled signal by factor N Interpolate signal..........i Interpolate (resample) to N points Print keyboard commands.....K prints this list Print signal report.........Q prints signal info and current settings Print isignal arguments.....W prints isignal (current arguments) Save output to disk.........O as .mat file with processed signal matrix Earlier versions
Earlier versions of iSignal as also available: Version 1.5 , Version 1.6, Version 1.7, Version 1.8, Version 1.9,Version 2.0, Version 2.4, Version 2.5, Version 2.6.
ProcessSignal,
a Matlab/Octave command-line function that performs smoothing and
differentiation on the time-series data set x,y (column or row
vectors). Type "help ProcessSignal". Returns the processed signal
as a vector that has the same shape as x, regardless of the shape of y.
The syntax is Processed=ProcessSignal(x,y,DerivativeMode,w,type,ends,Sharpen,factor1,factor2,SlewRate,MedianWidth)
May, 2013
Tom O'Haver
Professor Emeritus
Department of Chemistry and Biochemistry
The University of Maryland at College Park toh@umd.edu http://www.wam.umd.edu/~toh
PeakWidth4/700 for Lorentzian peaks), where PeakWidth is the full-width at half maximum of the peaks expressed in number of data points.
However, you don't need to do the math yourself; iSignal can calculate 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. You can expect a decrease in peak width (and corresponding increase in
peak height) of about 20% - 50%, depending on the shape of the peak (the peak area is largely uneffected by sharpening).
Excessive sharpening leads to baseline artifacts and increased noise. iSignal
allows you to experimentally determine the values of these parameters
that give the best trade-off between sharpening, noise, and baseline
artifacts, for your purposes. You can easily measure the effect of
sharpening quantitatively by turning on peak measure mode (press P) and then press E to toggle the sharpen mode off and on. Note:
In
iSignal version 1.9 and above, only the Savitzky-Golay smooth mode is
used for peak sharpening. Example shown in the figure on the right.
Peak and valley measurement
, such as 2,3, 4, etc). The I key replaces the signal with a linearily interploated version containing m
data points. This can be used either to increase or decrease the x-axis
interval of the signal or to convert unevenly spaced values to evenly
spaced values. After pressing C or I, you must type in the value of n or m respectively.
in the last four input arguments. 
perpendicular drop method, position the dotted red marker lines at
the minimum between the overlapped peaks. 