An S transformation at time t and frequency f has real and imaginary parts S(t,f)=ReS(t,f)+iImS(t,f)where i is the square root of minus 1. The cosine and sine of the phase angle at this time-frequency point are cosϕ(t,f)=ReS(t,f)/|S(t,f)|sinϕ(t,f)=ImS(t,f)/|S(t,f)|where the vertical bar pair indicates magnitude, here and below. The cosine and sine of phase angle are calculated from the S transformation without having to calculate the phase angle.
