Nulling systems often consist of a main channel and one or more auxiliary channels. In such systems, the degree of nulling achieved is often limited by mismatched frequency responses between the auxiliary channels and the main channel. The hybrid feedback technique is shown to compensate for this mismatch by enclosing the mismatched receiver components inside an adaptive feedback loop.>

The chirp Z-transform permits large bandwidth (i.e. high speed) analog devices to be used to compute the Discrete Fourier Transform (DFT). Such Implementations are often faster and/or smaller than all digital Fast Fourier Transforms (FFT's), but suffer from accuracy limitations imposed by the analog devices. In this paper, we present a nested algorithm that permits excess bandwidth of the analog device to be exploited in order to compute the DFT more accurately. The nested structure can be realized with a single analog device, and can be trained to the errors associated with the device. Algorithm performance is verified through computer simulations in which DFT accuracy is limited due to fixed tap weight errors in the FIR filter portion of the chirp Z-transform.

It is generally known that preservation of phase information in images is important as evidenced by the fact that modifying an image such that phase is preserved but the magnitude of all the spectral components is set to unity generally preserves many of the features of the original image. A similar experiment has been carried out with speech, showing that preservation of only the long-time phase retains many important features of the original speech. An interpretation of these results, and their potential application to blind deconvolution, is suggested.

A cryptographic system is described which is secure if and only if computing logarithms overGF(p)is infeasible. Previously published algorithms for computing this function requireO(p^{1/2})complexity in both time and space. An improved algorithm is derived which requiresO =(\log^{2} p)complexity ifp - 1has only small prime factors. Such values ofpmust be avoided in the cryptosystem. Constructive uses for the new algorithm are also described.