Monthly Archives: July 2020

KAY’s Single Frequency Estimator

As previously discussed, finding the frequency of a complex sinusoid embedded in noise is a classical problem in Signal Processing. The problem is compounded by the fact that number of samples available is usually quite small. So far, we have discussed Zero Crossing, FFT, MUSIC and ESPRIT methods of frequency estimation. Zero Crossing method is simplest of the above four but it can detect only one sinusoid at a time. Advantage of Zero Crossing method is that it is computationally not that complex. It does not require complex matrix manipulations as some of the other methods do.

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A Comparison of FFT, MUSIC and ESPRIT Methods of Frequency Estimation

As discussed in previous posts it is frequently required in communications and signal processing to estimate the frequency of a signal embedded in noise and interference. The problem becomes more complicated when the number of observations (samples) is quite limited. Typically, the resolution in the frequency domain is inversely proportional to the window size in the time domain. Sometimes the signal is composed of multiple sinusoids where the frequency of each needs to be estimated separately. Simple techniques such as Zero Crossing Estimator fail in such a scenario.  Even some advanced techniques such as MATLAB function “pwelch” fail to distinguish closely spaced sinusoids.

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