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The two symbols are used to distinguish between analog frequency (Upper case) and digital frequency (lower case) when using the bilinear transformation. The bilinear transformation distorts the frequencies because the entire jw axis is mapped onto the z plane unit circle, so it is necessary to distinguish between the two frequencies. Any textbook on DSP will explain this relationship. Look up “bilinear transform” in the index, or see
. https://www.ece.uvic.ca/~andreas/ISCASTutorial/Part 3-IIR Filters-Bilinear Transformation Method.pdf.
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