No, it is not necessary to normalize data if the variables have the same order of magnitude and have the same unit, for example a spectrum from a spectrometric method.
I guess it's about standardization...
Always remember that the standardization process involves loss of information, starting with basic data.
Furthermore, standardizing is an unnecessary procedure, when the data are expressed in the same unit of measure, unless they come from different populations or present evident discrepancies in the collection of the same data.
check your method - if the calculation uses the correlation matrix rather than the covariance matrix, the variables are scaled by default.
It really depends on the type of data you are working with. Normalization is a row-oriented transformation that puts all objects (variables) on an even footing. As a general rule, normalization should be applied in cases where the data are collected with a method where the detector signal is a function of sample mass (i.e. most GC detectors) or of source power (i.e. Raman spectroscopy) instead of sample concentration. Depending on the application, various normalization schemes can be employed (area normalization, peak normalization, mean normalization, range normalization, etc.).
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