Understanding of Fourier Transform, Laplace Transform and Z Transform

I recommend to learn the MIT open-course (Signal processing: Continuous and Discrete) by yourself. If you prefer watching the videos, you can go to 163 Open-course websites (Course Link is here).

Fourier Transform(FT) has a physical meaning: divide a continuous signal into the superposition of several sine waves and each sine wave can be represented by amplitude, frequency and phase. The signal after FT has its own amplitude spectrum and phase spectrum which are representing the distribution between amplitude and frequency, and the distribution between phase and frequency, respectively. In the real life, frequency has a very clear physical meaning. For example, the voice of men is very low and deep. This is because most components of their voice are low-frequency. Oppositely, the voice of women is very high and sharp. This is because their components are high-frequency mostly. For one signal, its time-domain representative and FT representative have the same information.

What is the function of FT?

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