[Introduction] [Signal arithmetic] [Signals and noise] [Smoothing] [Differentiation] [Peak Sharpening] [Harmonic analysis] [Fourier convolution] [Fourier deconvolution] [Fourier filter] [Wavelets] [Peak area measurement] [Linear Least Squares] [Multicomponent Spectroscopy] [Iterative Curve Fitting] [Hyperlinear quantitative absorption spectrophotometry] [Appendix and Case Studies] [Peak Finding and Measurement] [iPeak] [iSignal] [Peak Fitters] [iFilter] [iPower] [List of downloadable software] [Interactive tools]
The experimental signal in this case study had a number of narrow spikes above a seemingly flat baseline.
Using iSignal to investigate the signal, it was found that the visible positive spikes were single points of very large amplitude (up to 106), whereas the regions between the spikes were not really flat but contained bell-shaped peaks that were so much smaller (below 103) that they were not even visible on this scale. For example, using iSignal to zoom in to the region around x=26300, you can see one of those bell-shapes peaks with a small single-point negative-going spike artifact near its peak.
Other filter types, like most forms of smoothing, would be far less effective than a median filter for this type of artifact and would distort the peaks.
The negative spikes in this signal turned out to be steep steps, which can either be reduced by using iSignal's slew-rate limit function (the ` key) or manually eliminated by using the semicolon key (;) to set the selected region between the dotted red cursor lines to zero. Using the latter approach, the entire cleaned-up signal is shown below. The remaining peaks are all positive, bell shaped and have amplitudes from about 6 to about 750.
Note that fitting with an exponentially-broadened Gaussian model gives the peak parameters of the Gaussian before broadening. iSignal and iPeak estimate the peak parameters of the broadened peak. As before, the effect of the broadening is to shift the peak position to larger x values, reduce the peak height, and increase the peak width.
Position Height Width Area error
isignal 16871 788.88 32.881 27612 S/N=172
ipeak 16871 785.34 33.525 28029
peakfit(G) 16871 777.9 33.488 27729 1.68%
peakfit(E) 16863 973.72 27.312 28308 0.47%
G = Gaussian model;
E = Exponentially-broadened Gaussian model
page is part of "A Pragmatic Introduction to Signal
Processing", created and maintained by Prof. Tom O'Haver ,
Department of Chemistry and Biochemistry, The University of
Maryland at College Park. Comments, suggestions and questions
should be directed to Prof. O'Haver at email@example.com. Updated July, 2022.