Formant tracking using the wavelet-based DST

Speech signals vary rapidly with time. To track these changes in time, one requires a transform which maps time-magnitude signals into a time-frequency space representing the original signal. The Fourier transform (FT) is the standard time-to-frequency transform. The sine and cosine sinusoidal waves used by the FT have infinite support in t, and windowing is required to obtain any meaningful spatial information. Spatial resolution is therefore dependant on the extent of the window, the size of which is critical and varies from signal to signal depending on the anticipated frequency content. Wavelets use basis functions having finite support. The paper describes a new O(n) algorithm, which uses a non-orthogonal variant of the orthonormal Haar wavelet, to decompose signals into their approximate time-frequency space. The author shows that the algorithm, called the dominant scale transform (DST), can be used to track changing vowel formants with a very high spatial resolution.