In the last decade the work on linear tapped delay line equalizers has proved successful in reducing intersymbol interferenceone of the largest problems in data communication systems. An adjoining problem is the selection of a sampling time reference. An equalizer structure less sensitive to sampling time reference is studied for adaptive equalization. The equalization is simply done by means of tap coefficient adjustment. The equalizer consists of two parallel branches, each containing a transversal filter with adjustable tap coefficients. The branches are connected by a fixed filter, the transfer function of which is selected such that the equalizer can perform a sampling time reference displacement and a cancellation of intersymbol interference simultaneously. The criterion of goodness is the conventional meansquare error (including noise) between the actual output and a desired output. The equalizer is applied in two examples showing-in contrast to a conventional equalizer with the same total number of tap coefficients-the insensitivity of the minimum mean-square error (MMSE) to how the the sampling time reference is selected. Thus no extra circuits are needed for this purpose, while a mean-square error that is as low as the best that can be obtained with a conventional equalizer is adaptively maintained.

Frequency-shift-keying (FSK) signals with modulation indexm = 0.5have two significant properties. They have no discrete frequency components and nearly all the signal energy is contained within a narrow frequency region equal to\frac{3}{2}of the bit speed even without any band limiting. Unfortunately, a complete mathematical description of FSK signals in general is difficult, because FSK is a nonlinear process. A well-known exception is FSK withm = 1, because this signal can be described as the summation of two AM signals. This makes it easy to describe frequency- and time-domain properties. In this paper it is shown that by decomposing FSK signals withm = 0.5into two signals with well-understood spectral properties, it is possible to describe time- and frequency-domain properties and to calculate the effects of restricted bandwidth and linear distortion on the signal-space diagrams and eye patterns. Finally it is shown that duobinary FM can be treated as a special case of an FSK (m = 0.5) signal.