[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]

     

C. Buried treasure.

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.


Very narrow spikes like this are common artifacts in some experimental signals; they are easy to eliminate by using a median filter. The iSignal function has such a filter, activated by the "M" key. The result shows that the single-point spike artifacts have been eliminated, with little effect on the character of the bell-shaped 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.


iPeak can automate the measurement of peak positions and heights for the entire signal, using the peak detection settings shown at the bottom of the screen shot below.


If required, individual peaks can be measured more accurately by fitting the whole peak with iPeak's "N" key or with peakfit.m or ipf.m. The peaks are all slightly asymmetrical; they fit an exponentially-broadened Gaussian model to a fitting error less than about 0.5%, as shown on the left. The smooth residual plots suggests that the signal was smoothed before the spikes were introduced and that the noise increases with the signal amplitude (because these is little or noise on the base-line). . 


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

This 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 toh@umd.edu. Updated July, 2022.