Optimal design of discrete coefficient DFTs for spectral analysis

In the evaluation of the discrete Fourier transform (DFT) of a time signal, for spectral analysis, the main speed restricting factor is the multiplication by complex coefficients. The multiplier is also the most expensive hardware component. A scheme is proposed whereby these coefficients can be replaced by an optimum set, whose real and imaginary components are constrained such that multiplication becomes trivial. The optimum set of coefficients is found by representing each row of the DFT as a linear filter and then performing a frequency domain optimisation using mixed integer linear programming.