Fourier Transform
Today we extended the Fourier Series to non periodic loads introducing the Fourier Transform.
Having discussed the problems and the difficulties arising in the analytical treatment of Fourier Transform, we introduced the Discrete Fourier Transform. Particular stress was posed on the periodicity of the time and frequency representation of a signal, and on the problematic aspect of aliasing.
The different numerical techniques, known as Fast Fourier Transform, available to speed up DFT computation were presented.
Finally, we demonstrated the relationship between the impulse response function and the frequency response function, that is they are a Fourier transform pair.
Material available for this class:
- the slides i used for my lesson
- a ready to print version of the slides,
- a simple implementation of FFT, in Python.