Summary
This chapter has been another chapter on a specific mathematical technique. There have been a lot of formulae, particularly when it comes to learning about the various forms of Fourier decompositions. However, the formulae are not the key point here. Formulae can always be looked up. It is more important to understand and remember the concepts. Of these, the most important concepts we have covered are as follows:
- Why we decompose a function into a set of simpler building block functions.
- How a function can be decomposed using a set of basis functions, and how we can use the inner product between functions to calculate the coefficients or amplitudes in a decomposition.
- How to use an orthonormal basis as a convenient set of component functions to decompose a function,
. - The eigenfunctions of a linear operator and how they can naturally provide a complete orthonormal basis for decomposing other functions, .
- That a periodic function can be decomposed into...
