A five-sample digital FM-demodulator with application to multichannel TV sound

In the FM receiver we shall sample the input signal at a rate F = 4f/(2N+1) = sample rate, where f is close to the carrier frequency. Five successive samples a,b,c,d,e are delivered to an arithmetic unit executing a particular algorithm that the authors define. The parameter D in the algorithm is a very good approximation of the frequency deviation d. In fact, if the input signal is a sinewave with a frequency f+d, then D is strictly a function of d. A carrier FM-modulated by a low frequency sinewave with d < F/20, has harmonic distortion < 0.5%. Thus the algorithm interprets the five samples as if they were samples of a sinewave. An analysis predicts that the behavior of the demodulator is in all respects very similar to analog demodulators with limiters, e.g. quadrature detectors. Random and quantization nOise in the input yield a "triangular" output noise spectrum. Together with oversampling, this effect allows for rough quantization of the input. A practical problem with this demodulator is that a nonlinear a/d converter may cause beats. The main problem, however, is arithmetic: the need for a division with the square of the carrier envelope puts a round-off error limit to the dynamic range. However, this is of no concern if the carrier has a fairly constant amplitude, such as the SAP subcarrier in the composite BTSC signal.