Important Implications of FT

1. The energy of a signal f(x) can be defined as:

    This is called the Parceval's Theorem, it directly relates the energy of signal in time domain to the energy of signal in Fourier Transform domain.

2. Time-Frequency Uncertainty Principle

3. Graphic Representation of FT

http://research.opt.indiana.edu/library/fourierbook/ch12.html

4. Time-Frequency Localization
    It is important to localize the signal properties either in the time(spatial) domain or frequency domain for the convenience of an analysis.

5. Time-Frequency Uncertainty Principles

 





6. Sampling Theorem for Images