Discrete Fourier transforms, linear filters, and spectrum weighting

Computational procedures which have been developed in the past few years have taken the familiar frequency-domain techniques from the realm of theory and placed them in the realm of practice. In order to realize fully the potential of th techniques, it is necessary to gain insight into the physical significance of the discrete Fourier transform. Here, the discrete Fourier transform is viewed as a set of discrete linear filters--one filter for each Fourier coefficient. Each filter is seen to have zero poles and (N-1) zeros. (N is the number of data points transformed.) The characteristics of these filters are discussed. Spectrum weighting, for the purpose of sidelobe reduction, is also shown to be equivalent to discrete linear filtering. The filters in this case are similar to those which represent the discrete Fourier transform.