Abstract
In Chap. 1 we saw how a periodic function can be decomposed into a linear combination of sines and cosines, or equivalently, a linear combination of complex exponential functions. This kind of decomposition is, however, not very convenient from a computational point of view. The coefficients are given by integrals that in most cases cannot be evaluated exactly, so some kind of numerical integration technique needs to be applied. Transformation to the frequency domain, where meaningful operations on sound easily can be constructed, amounts to a linear transformation called the Discrete Fourier transform. We will start by defining this, and see how it can be implemented efficiently.
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Ryan, Ø. (2019). Digital Sound and Discrete Fourier Analysis. In: Linear Algebra, Signal Processing, and Wavelets - A Unified Approach. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-01812-2_2
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