Fourier Series and Transforms

We had a session on Fourier series and Transforms. In this session we gained insight about Transforms, their requirement, Fourier series, Fourier Transform, Difference between Laplace and Fourier Transform and most importantly, intuitive understanding of Fourier Series and Transform.

First of all we talked about Transforms. Transforms are methodology to change your perception towards the signal. There are number of transforms, each one of them is a method to change your perception about viewing Signals and Systems.

The main reason why Fourier Transforms is useful in almost all fields of Science and Technology is it gives us inner view of signal. It gives us the frequency range of all Sinusoidal waves that on adding up makes a signal. Hence, effectively we have to just study the behavior of system for generalized sinusoidal signals and hence we’ll be able to describe its output for any signals.

We discussed how to get feel about this transform and then slowly approached mathematical analysis. While preparing for the discussion we came across some interesting resources like http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/. This article taught us to be intuitive. While discussing its applications we have come across a recent patent by MIT known as “Eulerian Video Magnification”. We have discussed filters in frequency domain which can be explained as thresholding of frequencies. We concluded the session with understanding of Fourier Transforms in both ways, intuitively and mathematically.

Here is the Link of presentation of our meet.

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