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Attention is drawn to a number of possible variants in the detailed application of the coefficient matching technique to the computer synthesis of lumped linear networks. Tables of run times obtained with a numerical example provide some indication of the relative computational efficiency of the methods instanced. Simple closed form expressions for the optimum value of the multiplicative constant are derived for three variants; an illustrative table demonstrates that their use greatly improves the rate and range of convergence of the method.

This study is concerned with the information in zero crossings (ZC) of images. Logan's conditions, specifying when a one-dimensional signal may be recovered (within a multiplicative constant) from its ZC, are extended for various cases of two-dimensional signals. An algorithm is implemented in reconstruction of context-free band-pass images. It is also successfully applied in reconstruction of contextual images by first dissecting the image into appropriate bandpass-band-limited two-dimensional signals. In almost all cases of spectrum confined to less than an octave in one dimension, the reconstruction algorithm converges, whereas it does not converge for any signal exceeding one octave in bandwidth. This paper substantiates the proposition that images are well represented by the partial information confined to ZC.

An interesting subclass of bandpass signals {h} is described wherein the zero crossings of h determine h within a multiplicative constant. The members may have complex zeros, but it is necessary that h should have no zeros in common with its Hilbert transform h other than real simple zeros. It is then sufficient that the band be less than an octave in width. The subclass is shown to include full-carrier upper-sideband signals (of less than an octave bandwidth). Also it is shown that full-carrier lower-sideband signals have only real simple zeros (for any ratio of upper and tower frequencies) and, hence, are readily identified by their zero crossings. However, under the most general conditions for uniqueness, the problem of actually recovering h from its sign changes appears to be very difficult and impractical.

The concept of "bandwidth" is commonly used as a measure of the range of frequencies over which a network has an approximately constant gain. In this note the notion of bandwidth is extended to networks with arbitrary transfer characteristics. Specifically, it is defined in terms of the maximum allowable variance of the output of a network (to within a multiplicative constant) from that of an "ideal" network, the input being a band-limited signal. The maxum bandwidth of such an input signal is termed the bandwidth of the network under consideration.

The relationship between the K-pulse and the E-pulse is considered. Conditions are derived whereby the two waveforms differ, at most, by a multiplicative constant.