A Time Regularization Technique for Discrete Spectral Envelopes Through Frequency Derivative

In most applications of sinusoidal models for speech signal, an amplitude spectral envelope is necessary. This envelope is not only assumed to fit the vocal tract filter response as accurately as possible, but it should also exhibit slow varying shapes across time. Indeed, time irregularities can generate artifacts in signal manipulations or increase improperly the features variance used in statistical models. In this letter, a simple technique is suggested to improve this time regularity. Considering that time regularity is characterized by slowly varying spectral shapes among successive frames, the basic idea is to smooth the frequency derivative of the envelope instead of its absolute value. Even though, this idea could be applied to different envelope models, the present letter describes its application to the simple linear interpolation envelope. Using real speech signals, the evaluation shows that the time irregularity can be drastically reduced. Additional experiments using synthetic signals also show that the accuracy of the original envelope is not degraded by the process.