This paper deals with approximate methods for demodulating FM signals using their zero crossings. A first-order (linear) interpolation method is devised and analyzed. Computer programs were then prepared to compare this first-order interpolator to the more usual zero-order interpolator. Higher order interpolation is briefly discussed, and the results of using a second-order interpolator are compared to those using the lower order methods.

The relationship between the iterative techniques of Sandberg and Papoulis is clarified. The conditions of Sandberg's theorem are not satisfied in general when the problem is that of extrapolating a bandlimited signal outside of a known segment (a problem that is "illposed"). For an interesting special case, the iteration may be applied and the signal recovered exactly.

A method of recovering bandlimited signals from unequally spaced samples is described. The method uses an iterative procedure which requires low pass filtering of the unequally spaced sample pulses. This is followed by resampling at the same unequally spaced times and again low pass filtering to obtain a correction signal. Repeated application of this process is shown to converge to the original signal. These results are obtained by slight modifications of the analysis in Reference 2.

Since conventional FM demodulators are incapable of accurately demodulating very wide-band frequency-modulated signals, a new approach to the problem is needed. Based upon a theorem by Sandberg, a practical procedure is presented for demodulating not only typical FM signals but also those employing modulation bandwidths and/or frequency deviations on the order of the cartier frequency. The proposed demodulator utilizes an iterative recovery procedure. The first iteration is analogous to demodulation by a conventional zero crossing discriminator and results in severe distortion of the modulation under wide-band conditions. This distortion is reduced by successive iterations. Because, in practice, the iterative process is truncated after a finite number of terms, a procedure for computing the coefficients of these terms for minimum mean-squared error is given. Using computer simulation, the demodulation technique is demonstrated to work effectively for several very wide-band FM signals.