linear amplitude scaling, or, linear loudness scaling (with Excel)

history, inside the problem, the software, how to use, examples, donations
scaling n.1
Fig.1, amplification of 2nd data set to compare with first one


  Loudness scaling, amplitude scaling and linear scaling were used extensively in audio and sound analysis, in vibration analysis, in images analysis and in electronics for signal comparison.

  In this case we use those concepts in a different manner. Having 2 dataset coming from a measurement replicate or from a measure set with different instruments on the same sample, we make "amplification" of the 2nd data set to compare with the first one.

  In Fig.1 it is shown the problem, and on the upper right the solution with this software.

  Probably there are routines for Matlab/Octave and for "R" devoted to scaling your values. But it is still difficult for my students to grasp all parameters used in those routines and often the subtended errors.

  Accounting all I said previously, I have selected Excel to solve those small problems. As reference you can see:

  1. from M.D. Trifunac, CalTech University; the scaling is an important step in earthquake study, also in Fourier analysis,
  2. the book of Manthos G. Papadopoulos et al.; with title Linear-Scaling Techniques in Computational Chemistry and Physics,
  3. in the book of John Enderle at al.; you can find a simple description of linear scaling, in page 585 of Introduction to Biomedical Engineering,
  4. from T. Brand, University of Oldenburg; a congress presentation on Loudness Scaling in audio engineering field,

Inside the Problem

  In the Fig.1 you can see the blue line, the raw data. The main peak probably stays at 205nm with absorbance near 2.3 but the replicate shows low Abs value and to compare them we need an amplification of the purple spectra.

  Is better to spent some time on the blue-purple superimposition:

  1. if you obtain the "same" curve, in IC, in HPLC or in UV-Vis is better, the software is doing an artificial amplification, mathematical, surely with some distortion,
  2. always make a chart of the 2 curves, the first plot as comparison, the second plot to see what changes with different parameters setting,
  3. the 2 curves coming from different instruments or from replicates, so it is practically impossible superimposed, you must select if it is better to obtain the same values for highest peak, or as in Fig.1 produce a similar shoulder

The Software

  This free software was distributed under Creative Commons Public License, CCPL 3.0, see my Copyright web page. Please read accurately the Liability Waiver in red.

  There is only one version working on MS-Excel 2000, up to MS-Excel 2003, was tested on MS-Excel 2007 and 2010 version. Are available:


How To Use

  Dear students, this is not an Excel course, so you should already know how to use formulae and functions. I remember you to pass every lesson of Excel 2003 in this Course, and after that, do pass all the lessons of 2010 version (and do ALL projects).

  Very often the writer of the software is not the best writer of "instructions", he/she already knows how to use it! Nevertheless, I have made here a tentative to describe how proceed:

Fig.2, the Scaling parameter on the left with pointing cells, and the Solver options on the right


  As an example I have produced the file SCsources.xls . The columns B and C are an example, the columns D and E other one.

  The column B and C refer to an UV-Vis measurement campaign in the Roman Forum. The spring water of Lacus Iuturnae was measured with 100mm quartz suprasil cuvette, every 0.5 nm, with Lambda 16 Perkin Elmer spectrophotometer.

  The column D and E refer to an exercise with students on ancient dyes.

  For the 2 example the columns B and D are the references values, and the columns C and E are the data to be modified with scaling.


  If you know Excel you can expand or reduce the 1421 rows, and probably design a better solution.


Donations if you have a Bitcoin wallet

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Donations if you have not a Bitcoin wallet

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Universita' Degli Studi di Roma
La Sapienza
Dr. G. Visco
appointed professor for chemometrics & ....
Corso di Laurea in: Scienze Applicate ai Beni Culturali ed alla Diagnostica per la loro Conservazione

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