The Fast Fourier Transform algorithm exploits properties of the twiddle factor :
MH SET - 2019, SET Exam - 2019,
Answer: A
The FFT exploits the symmetry and periodicity of the twiddle factor.
The twiddle factor is \(W_{N} = e^{-j2\pi/N}\). It is periodic, \(W_{N}^{k+N} = W_{N}^{k}\), and symmetric, \(W_{N}^{k+N/2} = -W_{N}^{k}\). Using these properties, the FFT splits an N-point DFT into smaller DFTs and reuses products, cutting the work from about \(N^{2}\) complex multiplications to about \((N/2)\log_{2}N\).
Convolution, correlation, linearity and causality are properties of signals and systems, not of the twiddle factor, and 'asymmetry' is the opposite of the property used.
Please log in or register to report this question.