The multiwindow approach is a meaningful framework for nonparametric spectral estimation. It also encompasses several conventional methods as WOSA and frequency-averaged periodogram. Recently, some authors claimed that the Slepian windows of Thomson's method and other related optimal sets of windows show a better performance in terms of resolution, variance and leakage. In this paper, that claim is discussed by means of some simulation examples and by applying the various methods to speech recognition. In conclusion, frequency averaging of the periodogram is a computationally simple method that has a great flexibility for band specification and comparatively shows good performance. In fact, it is the spectral analysis technique most extensively employed for speech recognition.