Abstarct
The focus in the previous chapter was on the representation of finite groups by matrices and linear transformations (over the field of real or complex numbers). The related theory is very rich in content, and stands on its own as an area of study in mathematics. One could very justifiably ask at this point: What connections could group representation theory have with signal processing? The answer lies in relating the theory to what has been said in Chapters 1 and 4 about signals and systems.
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Notes
- 1.
Translation operators, as explained in Section ??, may be visualized as generalizations of the familiar delay lines of circuit and system theory. You may recall the way they are used in a transversal filter for simulating an LTI system with a given impulse response.
- 2.
- 3.
The real number field \(\mathbb{R}\) serves as an example. This point is also discussed in Marquis [12, p. 35].
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Sinha, V.P. (2010). Signal Processing and Representation Theory. In: Symmetries and Groups in Signal Processing. Signals and Communication Technology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9434-6_6
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