Fourier transforms with procedures such as Discrete Fourier Transforms and Fast Fourier Transforms
The Discrete Fourier Transform (DFT) converts a signal from:
The DFT of an N-point sequence produces:
The computational complexity of direct DFT is:
The Fast Fourier Transform (FFT) reduces complexity to:
The fundamental basis functions of DFT are:
Nyquist frequency is defined as:
Aliasing occurs when:
The inverse DFT (IDFT) is used to:
The FFT algorithm is based on:
Convolution in time domain corresponds to: