Real-time and Efficient Algorithms for Frequency Warping Based on Local Approximations of Warping Operators

Frequency warping is a modifier that acts on sound signals by remapping the frequency axis. Thus, the spectral content of the original sound is displaced to other frequencies. At the same time, the phase relationship among the signal components is altered, nonlinearly with respect to frequency. While this effect is interesting and has several applications, including in the synthesis by physical models, its use has been so far limited by the lack of an accurate and flexible real-time algorithm. In this paper we present methods for frequency warping that are based on local approximations of the warping operators and allow for real-time implementation. Filter bank structures are derived that allow for efficient realization of the approximate technique. An analysis of the error is also presented, which shows that both numerical and perceptual errors are within acceptable limits. Furthermore, the approximate implementation allows for a larger variety of warping maps than that achieved by the classical (non-causal) first-order allpass cascade implementation.