Original Publication Date: 1985-Apr-01
Included in the Prior Art Database: 2005-Feb-18
The Fourier transform, X, at a specific frequency, k, is a complex number which may be expressed in polar coordinates : X(k)=sqrt(real(X(k))*real(X(k)) + imag(X(k))*imag(X(k))) (1) P(k)=arctan(imag(X(k))/real(X(k))) (2) The quantity X(k) is referred to interchangeably as the gain, absolute value, or magnitude at frequency k. The quantity P(k) is referred to as the uncorrected phase at frequency k. Reference  presents an algorithm for calculating correct phase values from the raw phase values, P(k), which contain artifacts. Phase relations may be important in the synthesis of natural sounding speech, and particular speech sounds may contain characteristic phase signatures. In order to research these issues, however, an effective way of representing the phases in sound is needed.