Analytic complex wavelet packets for speech enhancement

In previous work, the authors found the lack of shift invariance of real wavelet packets very disadvantageous for speech enhancement in the case of periodic noise. Therefore, this paper investigates the positive properties of the dual-tree complex wavelet transform (DTCWT). This transform is nearly shift invariant at moderate additional computational cost. However, the straightforward approach of extending the DTCWT to wavelet packets by decomposing the high pass coefficients as well led to non-analytic basis functions. Because analytic basis functions were required for the desired properties, a filter swapping scheme was developed to preserve analyticity. This analytic complex wavelet packet transform showed improved denoising performance for the application of speech enhancement and promises improvements for other applications like general filtering and signal analysis.