Faster than fourier -- ultra-efficient time-to-frequency domain conversions for FDTD

Two highly efficient methods of computing magnitude and phase from time-domain data are demonstrated. These methods, based on solution of linear equations, are found to be equally accurate and more efficient than Fourier transform methods (DIT and FFT) for limited numbers of Frequencies. These methods provide a significant savings in computation time and storage requirements for FDTD simulations which require a large number of time-to-frequency domain conversions. Although some FDTD researchers may have applied the method for single frequency simulations, it is not widely known or used. The multiple frequency extension of this method has not been used previously, to my knowledge.