Comparison of various periodograms for sinusoid detection and frequency estimation

With the advent of the fast Fourier transform (FFT) algorithm, the periodog ram and its variants such as the Bartlett's procedure and Welch method, hav e become very popular for spectral analysis. However, there has not been a thorough comparison of the detection and estimation performances of these m ethods. Different forms of the periodogram are studied here for single real tone detection and frequency estimation in the presence of white Gaussian noise. The threshold effect in frequency estimation, that is, when the esti mation errors become several orders of magnitude greater than the Cramer-Ra o lower bound (CRLB), is also investigated. It is shown that the standard p eriodogram gives the optimum detection performance for a pure tone while th e Welch method is the best detector when there is phase instability in the sinusoid. As expected, since the conventional periodogram is a maximum like lihood estimator of frequency, it generally provides the minimum mean squar e frequency estimation errors.