Frequency-domain analysis of the interaction between a periodic and non periodic signal is performed using the Fourier or discrete-time Fourier transform. This requires the definition of Fourier and discrete-time Fourier transforms for periodic signals. In this lesson you will learn how impulses are used in the frequency domain to obtain Fourier transforms and discrete-time Fourier transforms for periodic signals that satisfies all the properties required of the respective transforms. You will learn how to use the series coefficients to find the transforms for periodic signals. Several examples illustrate this process and frequency-domain analysis of the interaction of a periodic signal and a linear, time invariant system.
The ability to represent periodic signals with the Fourier or discrete-time Fourier transform is a key skill for taking full advantage of the analysis power of the corresponding transforms.