A mathematical walkthrough of the Fourier transform, derived by extending Fourier series to non-periodic functions defined over an infinite interval. Covers the derivation via Riemann sum limits as the period tends to infinity, a worked example computing the transform of an odd triangular pulse, the frequency-domain interpretation of signals, existence conditions (absolute integrability), and key properties including linearity, scaling, time shifting, derivative transforms, and the convolution theorem. An appendix reviews Riemann sums and definite integrals.
Table of contents
Visualizing Fourier series for non-repeating functionsFourier series with L\rightarrow\infty leading to Fourier transformExample calculation of Fourier transformThe frequency domain representation of functionsExistence condition for the Fourier transformSome useful properties of Fourier transformsAppendix A: Riemann sum and the definite integral293 Impressions