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Speech signal consists of events in time and frequency, and therefore its analysis with high-resolution time-frequency tools is often of importance. Analytic filter bank provides a simple, fast, and flexible method to construct time-frequency representations of signals. Its parameters can be easily adapted to different situations from uniform to any auditory frequency scale, or even to a focused resolution. Since the Hilbert magnitude values of the channels are obtained at every sample, it provides a practical tool for a high-resolution time-frequency analysis. The present study describes the basic theory of analytic filters and tests their main properties. Applications of analytic filter bank to different speech analysis tasks including pitch period estimation and pitch synchronous analysis of formant frequencies and bandwidths are demonstrated. In addition, a new feature vector called group delay vector is introduced. It is shown that this representation provides comparable, or even better results, than those obtained by spectral magnitude feature vectors in the analysis and classification of vowels. The implications of this observation are discussed also from the speech perception point of view.