This correspondence presents the results of the enumeration of Costas arrays of order$27$: all arrays found, except for one, are accounted for by the Golomb and Welch construction methods.

It is pointed out that the time and frequency response of an FIR (finite-impulse response) filter are vectors mapped by the DFT (discrete Fourier transform) matrix. A vector space can be defined by expressing the DFT matrix in terms of the filter as a vector adjacent to the characteristic value matrix. For linear-phase filters, all operations and characteristic values are real, and design constraints in the time and frequency methods are given for computing the orthogonalized characteristic vector matrix, which is used in transforming the design constraints and in computing the filter weights. The procedure is efficient enough to be useful on personal computers.>

A general problem is addressed in which a real, continuous signal is to be sampled and its spectrum analyzed. It is shown that real sampling followed by an innovative complex first decimation filter stage minimizes the sample rate and produces minimum digital arithmetic or CCD hardware requirements. Only small differences distinguish broadband and narrow-band processing algorithms.

A technique is presented which allows an FFT to be performed in place without bit reverse index reordering either before or after the computation. This is done by combining the reordering operation with the first iteration of a decimation in time FFT. Typical savings are 10 percent.