Spectral Envelope Recovery beyond the Nyquist Limit for High-Quality Manipulation of Speech Sounds

A simple new method to recover details in a spectral envelope is proposed based on a recently introduced speech analysis, modification and resynthesis framework called TANDEM-STRAIGHT. Spectral envelope recovery of voiced sounds is a discrete-to-analog conversion in the frequency domain. However, there is a fundamental problem because the spatial frequency contents of vocal tract functions generally exceed the Nyquist limit of the equivalent sampling rate determined by the fundamental frequency. TANDEM-STRAIGHT yields a method to recover a spectral envelope based on the consistent sampling theory and provides base information for exceeding this limit. At the final stage, the AR spectral envelope estimated from the TANDEM-STRAIGHT spectrum is divided by the F0 adaptively smoothed version of itself to supply the missing high-spatial-frequency details of the envelope. The underlying principle of the proposed method can also be applied to other speech synthesis frameworks.