Starts with concept of a frequency function as an ordered list of Fourier series coefficients. Summary of derivation of Fourier transform from complex Fourier series and development of frequency-function ideas. Introduction of the Dirac delta function as the Fourier transform of a sinusoid to set context for characteristics of the discrete Fourier transform (DFT) spectrum. Intuitive derivation of DFT from Fourier series of piecewise-approximated sampled continuous data. Symmetry and linearity of Fourier transform and DFT. Frequency resolution of DFT, sampling theorem and Nyquist frequency. Fast Fourier Transform (FFT) as optimised DFT algorithms.