https://www.farewellway.com/Farewell Way!This is a personal webpage designed to link content created on other platforms and organize thoughts and research on technical topics. The webpage is intended to reflect a personal way of learning and understanding things, with the aim of creating a comprehensive resource for both the owner and visitors to the site. 2024-06-21T18:16:31+00:00 Alberto Simon https://www.farewellway.com/ Jekyll © 2024 Alberto Simon /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png Considerations about Fourier series and Spectrum2024-06-14T08:00:00+00:00 2024-06-14T08:00:00+00:00 https://www.farewellway.com/posts/Fourier-Series-Considerations-about-spectrum/ Alberto Simon This final conclussions lesson can be accomodated to the last 10 to 15 minutes of a lesson. Considerations about Fourier series and Spectrum Decomposition of Functions The underlying idea behind series is to decompose a sum of simpler functions. If we sum all the obtained sinusoidal functions, we get a function of the same shape. Linear Combination of Frequencies When calculating the Fourier... Example of Fourier series of an asymmetrical square pulse train2024-06-14T05:15:00+00:00 2024-06-14T05:15:00+00:00 https://www.farewellway.com/posts/Fourier-Series-Example-Pulse-Train-Asymmetrical/ Alberto Simon This example can be developed on the blackboard for 10 to 15 minutes. Example: Fourier $d_n$ coefficients of an asymmetrical square pulse train Problem Statement Find the coefficients for the Fourier series of the signal $f(t)$ Approach Pulse Train The signal is a pulse train, as in previous example, but in this case, the pulse occupies one-fifth of the train; or in other words, one-tenth ... Example of Fourier series of a symmetrical bipolar square pulse train2024-06-13T11:55:00+00:00 2024-06-14T08:53:17+00:00 https://www.farewellway.com/posts/Fourier-Series-Example-Pulse-Train-Symmetrical-Biased/ Alberto Simon This example can be developed on the blackboard for 20 to 30 minutes, if followed by a previous exmample. Example: Fourier series of a symmetrical bipolar square pulse train Problem Statement Develop the Fourier series of the signal $g(t)$ Approach Periodic Alternating Function The function is periodic; the value alternates between 1 and -1. Choice of Period The function resembles a sine ... Example of Fourier series of a symmetrical square pulse train2023-06-15T12:55:00+00:00 2024-06-14T08:53:17+00:00 https://www.farewellway.com/posts/Fourier-Series-Example-Pulse-Train-Symmetrical/ Alberto Simon This example can be developed on the blackboard for 30 to 50 minutes, depending on how thorough the explanations given to the students are. Example: Fourier series of a symmetrical square pulse train Problem Statement Develop the Fourier series of the signal $f(t)$. Approach Signal characteristics We have a periodic time function, which could be generated by a square wave oscillator. It’s ... Fourier Series2023-06-15T12:28:00+00:00 2023-06-15T12:28:00+00:00 https://www.farewellway.com/posts/Fourier-Series-in-action/ Alberto Simon This is the content of an introductory lesson to Signals. Inmersive content about Fourier series and how to apply the formulae. Time: Exposition time: about 10 minutes and then go through the practical examples. Fourier series in action Fourier Transform and Periodicity Are Fourier transforms only useful for periodic functions? No. A Fourier transform completely defines a periodic function, b...