Choice of the acquisition parameters for frequency estimation of a sine wave by interpolated DFT method

The accuracy of the frequency estimation of a sine wave corrupted by quantization noise using the Interpolated Discrete Fourier Transform (IpDFT) method is affected by systematic and random errors. The systematic errors are independent of quantization noise and are due to the interferences from the image parts of the sine wave spectrum. They depend of the acquisition parameter – integer number of recorded sine wave cycles. The random errors are due to the quantization noise and depend on the acquisition parameter – number of acquired samples. In this paper for the situations in which the IpDFT method uses the maximum side lobe decay windows a condition for the integer part of the number of recorded sine wave cycles is derived to ensure that the systematic errors are very small compared with the quantization errors. Also, a condition for the number of samples is derived to ensure that the absolute error of the normalized frequency due to the random errors is smaller than a desired value with a high confidence level. Carried out simulations confirm the validity of each derived condition.