← Back

Fourier at a Glance: Continuous vs. Discrete, Series vs. Transform

Posted on 14 November 2011.

When I co-lectured ENEE322: Signal and System Theory, I wrote this handout as a complement to Oppenheim and Willsky.

Table 4.1: Comparison of Fourier Operations

In particular, Table 4.1 on page 14, pictured above, shows the relationships between the continuous-time Fourier series (CTFS), discrete-time Fourier series (DTFS), continuous-time Fourier transform (CTFT), and discrete-time Fourier transform (DTFT). Note the similarities and differences among the four operations:

My motive behind writing these notes was to present the most important concepts from Oppenheim and Willsky as concisely as possible. Often, textbooks sacrifice clarity for depth. Here, I present the main concepts from separate chapters as close together as possible so that students can more easily discover the relationships between concepts rather than studying each chapter in isolation.

For anyone taking or teaching signal processing, please feel free to use these notes as you wish, and let me know what you think!

(This post was inspired by this answer that I posted to dsp.stackexchange.com.)