Bootstrap-based frequency estimation method

In this paper, the bootstrap method was used to estimate the frequency of a signal. Here, the periodic signal was transformed into a rectangular wave and the interval of time between two consecutive positive edges of this rectangular wave was estimated. First, in order to estimate this interval of time, a counter was used to count the number of clock pulses that have occurred during every interval of this type. In this case, the clock frequency was the sampling frequency. Next, this process was repeated several times and a vector of estimated values of the period of the signal was created. After that, this vector was considered as a random sample and it was used to create thousands of resamples with the same size as the above-mentioned random sample and that were created by sampling with replacement from the original random sample. Then, for each resample, the sample mean was calculated and the inverse of the mean of these sample means was used as an estimation of the frequency of the signal. Finally, a prototype of this statistic method to frequency estimation was built. The results of the experiment were satisfactory.