Is there any alternative basis for a fourier-like transform?

1. What are the based methods of Fourier transform?
2. Is FFT and DFT same?
3. What is the basis function of the Fourier transform?

What are the based methods of Fourier transform?

Fourier transform methods allow the analysis of complex waveforms in terms of their sinusoidal components [32]. Fourier analysis transforms a waveform into its spectral components and has been utilized in mass spectrometry, infrared spectrometry, and nuclear magnetic resonance.

Is FFT and DFT same?

It is important to note that while computationally dif- ferent, the FFT algorithm is functionally equivalent to the DFT; it simply achieves computational savings by exploiting symmetries in the definition of the DFT.

What is the basis function of the Fourier transform?

The Fourier basis function is method to smooth out data varying over a continuum and exhibiting a cyclical trend. Smoothing techniques play an important role in Functional Data Analysis (FDA) as they provide insight in the functional behavior of stochastic process.