This paper proposes a method for precisely estimating sinusoidal frequency using five samples. The estimation procedure is implemented by interpolating the impulse location between DFT results. Five samples are used because two complex components are available in the DFT results. However, an estimation method which uses four samples and is called Prony's approximation method is known in the literature. To derive interpolation formulas for six or more samples is more complex. In this paper, strict estimation formulas and their simplified versions are deduced from the DFTs of five samples. The frequency estimation error is also discussed with a computer‐simulated experiment which shows a 1 percent r.m.s. error at a signal‐to‐noise ratio of 30 dB. This method may be applicable for representing frequency in a direct binary form which can be processed by simple operations such as addition, exclusive‐OR, and sign extractions form the calculated value.

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A method of straightforward conversion of sinusoidal frequency to Gray code expression is described. The unknown frequency is estimated using only the sign of the inverse cosine function. The frequency conversion error is shown by computer experiment. For a more accurate result, the majority decision principle and threshold logic, that is, a maximum likelihood estimator, are applied. Hardware implementation is so easy that the whole system can be implemented on an LSI chip.

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