A NONMYSTICAL TREATMENT OF TAPE SPEED COMPENSATION FOR FREQUENCY MODULATED SIGNALS

Abstract

In this paper, the problem of non-constant tape speed is examined for frequency modulated signals. Frequency modulation and demodulation are briefly reviewed. Tape speed variation is modeled as a distortion of the independent variable of a frequency modulated signal. This distortion produces an additive amplitude error in the demodulated message which is comprised of two terms. Both depend on the derivative of time base error, which is the flutter of the analog tape machine. The first term depends on the channel’s center frequency and frequency deviation constant as well as flutter, while the second depends solely on the message and flutter. The relationship between the additive amplitude error and manufacturer’s flutter specification is described. Relative errors and signal-to-noise ratios are discussed for the case of a constant message to gain insight as to when tape speed variation will cause significant errors. An algorithm which theoretically achieves full compensation of tape speed variation is developed. The algorithm is confirmed via spectral computations on laboratory data. Finally, the algorithm is applied to field data. The reference is a temperature signal which is a non-zero constant, and the message is a pressure signal. The spectrum of the uncompensated message is clearly contaminated by the additive amplitude error, whereas the spectrum of the compensated message is not. Incorporation of this algorithm into the data-playback/data-reduction procedures is shown to greatly improve the measurement signal accuracy and quality. The treatment is nonmystical in that all derivations are directly tied to the fundamental equations describing frequency modulation and demodulation.