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Periodically structured noise is noise which occurs randomly but with a fixed or slowly varying period. The noise periodicity is usually due to some underlying process, such as block processing of the speech where discontinuities between successive blocks result. This type of noise permeates the entire speech spectrum and is not removable by standard filtering techniques. The recently developed time domain harmonic sealing (TDHS) algorithm has been found to be the basis for an effective enhancement technique. In this paper we discuss the underlying theory of this technique and establish a class of windows for its implementation. As an example the frame rate noise of adaptive transform coding was perceptually reduced using this technique. Results from a subjective testing experiment using ATC coded speech with bit rates of 7.2 to 16 Kb/s indicated an improvement in quality equivalent to an increase in code rate of 2.4 to 3 Kb/s for speech originally coded at 7.2 to 12 Kb/s.