The intuition behind Fourier and Laplace transforms I was never taught in school

The video tutorial explains the Fourier transform, focusing on its geometric intuition and visual representation using cosine and sine functions. It covers how to calculate the magnitude and phase of the transform and provides examples with cosine functions and square waves. The tutorial also introduces the concept of a continuous spectrum of sinusoids and briefly discusses the Laplace transform, highlighting its ability to analyze both sinusoidal and exponential components in signals.

Explain the concept of infinite area in the context of the Fourier transform.

What is the relationship between the Fourier transform and periodic functions?

What role does the Laplace transform play in relation to the Fourier transform?

How can we interpret the Fourier transform as a scanner for sinusoids?