A matched filter system is described which was designed to detect complicated signals subject to a wide range of possible Doppler shifts. A 100 tap band-pass delay line was used in conjunction with a resistor weighting matrix to synthesize signals and filter characteristics. The system could handle a signal with a duration-bandwidth product of 100 over a range of Doppler frequency shifts 17 times the reciprocal of the signal duration. A theoretical discussion of the Doppler effect is given, making use of conjugate functions or Hilbert Transforms. Various engineering compromises which simplify the construction of matched filters are suggested. The performance of the resulting signal detection system was within 5 db of that of an ideal theoretical model.

As the communication art becomes more sophisticated, engineers are being called on to deal more and more with complicated signals. This trend is typified by the use of noise-like signals to combat multipath (as in the RAKE), various suggestions for improving the range and velocity resolution of radars, and the desire to evolve ways of reducing the complication of a signal (as in the case of narrow band coding schemes for speech). As yet, however, no set of analytical tools has been developed which make the behavior of such complicated signals both easy to compute and simple to understand. This paper reviews some of the techniques which have been evolved for dealing with signals, and the difficulties that arise in using them; it then generalizes a unit-function procedure first suggested by Gabor into flexible procedure for picturing and computing the behavior of complicated signals.

A loss of signal detectability results from ideal symmetric limiting of a very narrow-band signal in narrow-band Gaussian noise. At small input snr this loss can be expressed in terms of the degradation of the effective signal energy-to-noise power per cycle ratio. Proceeding from results derived previously by Davenport and Price, an expression is derived for this degradation in terms of the autocorrelation function of the input noise. The degradation is evaluated for three typical input noise autocorrelation functions and is found to be quite small in all these cases. It is seen that the degradation can be made to vanish by appropriately shaping the spectrum of the input noise. Regulation of the input noise spectrum to obtain conditions of limiter operation assumed in this paper may often prove to be a convenient method for reducing loss of signal detectability in band-pass limiters.