Comment by zadwang

Fourier basis is unique in that the complex exponential basis functions are the eigen vectors of the linear time invariant (LTI) systems. No other transform has this property. Many real world systems (circuits, communication channels, antennas, etc) are LTI. This property make sure for example, signals transmitted over different frequencies do not interfere. That is why Fourier transform is so useful and used instead of other transforms. There is also the connection with quantum physics, in using Fourier pair as wave functions of position and momentum, which other transforms don’t have.